Properties

Label 7605.2.a
Level $7605$
Weight $2$
Character orbit 7605.a
Rep. character $\chi_{7605}(1,\cdot)$
Character field $\Q$
Dimension $259$
Newform subspaces $77$
Sturm bound $2184$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7605.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 77 \)
Sturm bound: \(2184\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7605))\).

Total New Old
Modular forms 1148 259 889
Cusp forms 1037 259 778
Eisenstein series 111 0 111

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(5\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(26\)
\(+\)\(+\)\(-\)\(-\)\(26\)
\(+\)\(-\)\(+\)\(-\)\(26\)
\(+\)\(-\)\(-\)\(+\)\(26\)
\(-\)\(+\)\(+\)\(-\)\(42\)
\(-\)\(+\)\(-\)\(+\)\(36\)
\(-\)\(-\)\(+\)\(+\)\(35\)
\(-\)\(-\)\(-\)\(-\)\(42\)
Plus space\(+\)\(123\)
Minus space\(-\)\(136\)

Trace form

\( 259 q + q^{2} + 261 q^{4} - q^{5} + 4 q^{7} + 9 q^{8} + O(q^{10}) \) \( 259 q + q^{2} + 261 q^{4} - q^{5} + 4 q^{7} + 9 q^{8} - 3 q^{10} - 20 q^{14} + 261 q^{16} - 6 q^{17} + 4 q^{19} - 7 q^{20} + 16 q^{22} + 259 q^{25} + 12 q^{28} + 10 q^{29} - 12 q^{31} - 11 q^{32} + 2 q^{34} + 4 q^{35} + 10 q^{37} - 3 q^{40} - 18 q^{41} + 12 q^{43} - 28 q^{44} + 32 q^{46} + 4 q^{47} + 275 q^{49} + q^{50} + 10 q^{53} + 4 q^{55} - 40 q^{56} + 6 q^{58} - 4 q^{59} - 22 q^{61} + 241 q^{64} + 24 q^{67} - 6 q^{68} - 8 q^{70} + 16 q^{71} + 14 q^{73} + 22 q^{74} + 48 q^{76} + 20 q^{77} + 12 q^{79} - 15 q^{80} - 42 q^{82} - 32 q^{83} - 10 q^{85} + 76 q^{86} + 52 q^{88} + 2 q^{89} + 20 q^{92} - 60 q^{94} + 12 q^{95} + 18 q^{97} - 31 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7605))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 13
7605.2.a.a 7605.a 1.a $1$ $60.726$ \(\Q\) None \(-2\) \(0\) \(1\) \(5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}+5q^{7}-2q^{10}+\cdots\)
7605.2.a.b 7605.a 1.a $1$ $60.726$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}-4q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.c 7605.a 1.a $1$ $60.726$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.d 7605.a 1.a $1$ $60.726$ \(\Q\) None \(-1\) \(0\) \(-1\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+2q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.e 7605.a 1.a $1$ $60.726$ \(\Q\) None \(-1\) \(0\) \(-1\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.f 7605.a 1.a $1$ $60.726$ \(\Q\) None \(-1\) \(0\) \(-1\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.g 7605.a 1.a $1$ $60.726$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}-4q^{11}+\cdots\)
7605.2.a.h 7605.a 1.a $1$ $60.726$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}+4q^{11}+\cdots\)
7605.2.a.i 7605.a 1.a $1$ $60.726$ \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{5}-3q^{7}-3q^{11}+4q^{16}+\cdots\)
7605.2.a.j 7605.a 1.a $1$ $60.726$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{5}+q^{7}+3q^{11}+4q^{16}+\cdots\)
7605.2.a.k 7605.a 1.a $1$ $60.726$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{5}+q^{7}+6q^{11}+4q^{16}+\cdots\)
7605.2.a.l 7605.a 1.a $1$ $60.726$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}-q^{7}-6q^{11}+4q^{16}+\cdots\)
7605.2.a.m 7605.a 1.a $1$ $60.726$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}+q^{7}-3q^{11}+4q^{16}+\cdots\)
7605.2.a.n 7605.a 1.a $1$ $60.726$ \(\Q\) None \(0\) \(0\) \(1\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}+3q^{7}+3q^{11}+4q^{16}+\cdots\)
7605.2.a.o 7605.a 1.a $1$ $60.726$ \(\Q\) None \(1\) \(0\) \(1\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-4q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.p 7605.a 1.a $1$ $60.726$ \(\Q\) None \(1\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.q 7605.a 1.a $1$ $60.726$ \(\Q\) None \(1\) \(0\) \(1\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.r 7605.a 1.a $1$ $60.726$ \(\Q\) None \(1\) \(0\) \(1\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.s 7605.a 1.a $1$ $60.726$ \(\Q\) None \(2\) \(0\) \(-1\) \(-5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}-5q^{7}-2q^{10}+\cdots\)
7605.2.a.t 7605.a 1.a $1$ $60.726$ \(\Q\) None \(2\) \(0\) \(-1\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}+q^{7}-2q^{10}+\cdots\)
7605.2.a.u 7605.a 1.a $1$ $60.726$ \(\Q\) None \(2\) \(0\) \(1\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots\)
7605.2.a.v 7605.a 1.a $1$ $60.726$ \(\Q\) None \(2\) \(0\) \(1\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}+3q^{7}+2q^{10}+\cdots\)
7605.2.a.w 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{13}) \) None \(-4\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-\beta q^{7}-2q^{10}+\cdots\)
7605.2.a.x 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-2+\cdots)q^{7}+\cdots\)
7605.2.a.y 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.z 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+q^{5}+\beta q^{7}+\cdots\)
7605.2.a.ba 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(-2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(3-2\beta )q^{7}+\cdots\)
7605.2.a.bb 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(-2\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}-q^{5}+q^{7}-3q^{8}+\cdots\)
7605.2.a.bc 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{17}) \) None \(-1\) \(0\) \(-2\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(-1-\beta )q^{7}+\cdots\)
7605.2.a.bd 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{17}) \) None \(-1\) \(0\) \(-2\) \(5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(3-\beta )q^{7}+\cdots\)
7605.2.a.be 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-q^{5}-2q^{7}-\beta q^{8}-\beta q^{10}+\cdots\)
7605.2.a.bf 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-3+2\beta )q^{7}+\cdots\)
7605.2.a.bg 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}+q^{5}-q^{7}+3q^{8}+\cdots\)
7605.2.a.bh 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(2\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(1+\beta )q^{7}+\cdots\)
7605.2.a.bi 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(2\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(3-\beta )q^{7}+\cdots\)
7605.2.a.bj 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}-q^{5}+\beta q^{7}+\cdots\)
7605.2.a.bk 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+q^{5}+(1-2\beta )q^{7}+\cdots\)
7605.2.a.bl 7605.a 1.a $2$ $60.726$ \(\Q(\sqrt{13}) \) None \(4\) \(0\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}+\beta q^{7}-2q^{10}+\cdots\)
7605.2.a.bm 7605.a 1.a $3$ $60.726$ \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2})q^{2}+(4-\beta _{1})q^{4}+\cdots\)
7605.2.a.bn 7605.a 1.a $3$ $60.726$ \(\Q(\zeta_{14})^+\) None \(-2\) \(0\) \(-3\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
7605.2.a.bo 7605.a 1.a $3$ $60.726$ \(\Q(\zeta_{14})^+\) None \(-1\) \(0\) \(-3\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bp 7605.a 1.a $3$ $60.726$ \(\Q(\zeta_{14})^+\) None \(-1\) \(0\) \(3\) \(-12\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}-4q^{7}+(-1+\cdots)q^{8}+\cdots\)
7605.2.a.bq 7605.a 1.a $3$ $60.726$ \(\Q(\zeta_{14})^+\) None \(-1\) \(0\) \(3\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.br 7605.a 1.a $3$ $60.726$ \(\Q(\zeta_{14})^+\) None \(-1\) \(0\) \(3\) \(5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
7605.2.a.bs 7605.a 1.a $3$ $60.726$ 3.3.564.1 None \(-1\) \(0\) \(3\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1+\beta _{2})q^{7}+\cdots\)
7605.2.a.bt 7605.a 1.a $3$ $60.726$ 3.3.148.1 None \(0\) \(0\) \(-3\) \(5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)
7605.2.a.bu 7605.a 1.a $3$ $60.726$ 3.3.148.1 None \(0\) \(0\) \(3\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.bv 7605.a 1.a $3$ $60.726$ 3.3.756.1 None \(0\) \(0\) \(-3\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bw 7605.a 1.a $3$ $60.726$ 3.3.756.1 None \(0\) \(0\) \(3\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bx 7605.a 1.a $3$ $60.726$ 3.3.316.1 None \(0\) \(0\) \(-3\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(3+\beta _{2})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots\)
7605.2.a.by 7605.a 1.a $3$ $60.726$ \(\Q(\zeta_{14})^+\) None \(1\) \(0\) \(-3\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bz 7605.a 1.a $3$ $60.726$ \(\Q(\zeta_{14})^+\) None \(1\) \(0\) \(-3\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(1-\beta _{1})q^{7}+\cdots\)
7605.2.a.ca 7605.a 1.a $3$ $60.726$ \(\Q(\zeta_{14})^+\) None \(1\) \(0\) \(-3\) \(12\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+4q^{7}+(1-2\beta _{1}+\cdots)q^{8}+\cdots\)
7605.2.a.cb 7605.a 1.a $3$ $60.726$ \(\Q(\zeta_{14})^+\) None \(1\) \(0\) \(3\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(1+\beta _{1})q^{7}+\cdots\)
7605.2.a.cc 7605.a 1.a $3$ $60.726$ 3.3.564.1 None \(1\) \(0\) \(-3\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
7605.2.a.cd 7605.a 1.a $3$ $60.726$ \(\Q(\zeta_{14})^+\) None \(2\) \(0\) \(3\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
7605.2.a.ce 7605.a 1.a $3$ $60.726$ \(\Q(\zeta_{14})^+\) None \(3\) \(0\) \(-3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}-q^{5}+\cdots\)
7605.2.a.cf 7605.a 1.a $4$ $60.726$ 4.4.4752.1 None \(-2\) \(0\) \(4\) \(10\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+(3+\beta _{2}+\cdots)q^{7}+\cdots\)
7605.2.a.cg 7605.a 1.a $4$ $60.726$ 4.4.7488.1 None \(-2\) \(0\) \(-4\) \(6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}-q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.ch 7605.a 1.a $4$ $60.726$ 4.4.13824.1 None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
7605.2.a.ci 7605.a 1.a $4$ $60.726$ 4.4.13824.1 None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
7605.2.a.cj 7605.a 1.a $4$ $60.726$ 4.4.4752.1 None \(2\) \(0\) \(-4\) \(-10\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+(-3+\cdots)q^{7}+\cdots\)
7605.2.a.ck 7605.a 1.a $4$ $60.726$ 4.4.7488.1 None \(2\) \(0\) \(4\) \(-6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.cl 7605.a 1.a $5$ $60.726$ 5.5.3352656.1 None \(-2\) \(0\) \(-5\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-\beta _{4}q^{7}+\cdots\)
7605.2.a.cm 7605.a 1.a $5$ $60.726$ 5.5.3352656.1 None \(-2\) \(0\) \(-5\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{4}q^{7}+\cdots\)
7605.2.a.cn 7605.a 1.a $5$ $60.726$ 5.5.3352656.1 None \(2\) \(0\) \(5\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-\beta _{4}q^{7}+\cdots\)
7605.2.a.co 7605.a 1.a $5$ $60.726$ 5.5.3352656.1 None \(2\) \(0\) \(5\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+\beta _{4}q^{7}+\cdots\)
7605.2.a.cp 7605.a 1.a $9$ $60.726$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-3\) \(0\) \(-9\) \(7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{6})q^{2}+(2-\beta _{3}-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
7605.2.a.cq 7605.a 1.a $9$ $60.726$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(0\) \(-9\) \(-10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{7}q^{2}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
7605.2.a.cr 7605.a 1.a $9$ $60.726$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(0\) \(9\) \(10\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{7}q^{2}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
7605.2.a.cs 7605.a 1.a $9$ $60.726$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(3\) \(0\) \(9\) \(-7\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{6})q^{2}+(2-\beta _{3}-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
7605.2.a.ct 7605.a 1.a $10$ $60.726$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(10\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}+(1+\beta _{5})q^{4}+q^{5}+\beta _{9}q^{7}+\cdots\)
7605.2.a.cu 7605.a 1.a $10$ $60.726$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(0\) \(-10\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+(1+\beta _{5})q^{4}-q^{5}+\beta _{9}q^{7}+\cdots\)
7605.2.a.cv 7605.a 1.a $12$ $60.726$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(0\) \(12\) \(-12\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.cw 7605.a 1.a $12$ $60.726$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(0\) \(12\) \(12\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}+q^{5}+(1+\cdots)q^{7}+\cdots\)
7605.2.a.cx 7605.a 1.a $12$ $60.726$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(0\) \(-12\) \(-12\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.cy 7605.a 1.a $12$ $60.726$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(0\) \(-12\) \(12\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7605))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7605)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(585))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(845))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1521))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2535))\)\(^{\oplus 2}\)