Properties

Label 7360.2.a
Level $7360$
Weight $2$
Character orbit 7360.a
Rep. character $\chi_{7360}(1,\cdot)$
Character field $\Q$
Dimension $176$
Newform subspaces $74$
Sturm bound $2304$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 7360 = 2^{6} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7360.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 74 \)
Sturm bound: \(2304\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7360))\).

Total New Old
Modular forms 1176 176 1000
Cusp forms 1129 176 953
Eisenstein series 47 0 47

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

\(2\)\(5\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(22\)
\(+\)\(+\)\(-\)\(-\)\(22\)
\(+\)\(-\)\(+\)\(-\)\(25\)
\(+\)\(-\)\(-\)\(+\)\(19\)
\(-\)\(+\)\(+\)\(-\)\(22\)
\(-\)\(+\)\(-\)\(+\)\(22\)
\(-\)\(-\)\(+\)\(+\)\(19\)
\(-\)\(-\)\(-\)\(-\)\(25\)
Plus space\(+\)\(82\)
Minus space\(-\)\(94\)

Trace form

\( 176 q + 176 q^{9} + O(q^{10}) \) \( 176 q + 176 q^{9} - 32 q^{13} - 32 q^{21} + 176 q^{25} + 32 q^{33} - 32 q^{37} + 32 q^{41} + 176 q^{49} + 32 q^{57} - 32 q^{61} + 208 q^{81} + 16 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7360))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 23
7360.2.a.a 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(-3\) \(-1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{5}+2q^{7}+6q^{9}-q^{13}+\cdots\)
7360.2.a.b 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(-3\) \(1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}+2q^{7}+6q^{9}+3q^{13}+\cdots\)
7360.2.a.c 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(-2\) \(-1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots\)
7360.2.a.d 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(-2\) \(1\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}-3q^{7}+q^{9}+6q^{11}+\cdots\)
7360.2.a.e 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(-2\) \(1\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}-2q^{15}+\cdots\)
7360.2.a.f 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(-2\) \(1\) \(5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+5q^{7}+q^{9}-2q^{11}+\cdots\)
7360.2.a.g 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{9}+2q^{11}+5q^{13}+\cdots\)
7360.2.a.h 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}-2q^{9}-4q^{11}+\cdots\)
7360.2.a.i 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-4q^{7}-2q^{9}+6q^{11}+\cdots\)
7360.2.a.j 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(-1\) \(1\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}-2q^{9}-q^{13}-q^{15}+\cdots\)
7360.2.a.k 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-3q^{9}-6q^{11}+2q^{13}+\cdots\)
7360.2.a.l 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-3q^{9}+6q^{11}+2q^{13}+\cdots\)
7360.2.a.m 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-3q^{9}-6q^{11}-6q^{13}+\cdots\)
7360.2.a.n 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-3q^{9}+2q^{11}+2q^{13}+\cdots\)
7360.2.a.o 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
7360.2.a.p 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
7360.2.a.q 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-3q^{9}-2q^{11}+2q^{13}+\cdots\)
7360.2.a.r 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-3q^{9}+6q^{11}-6q^{13}+\cdots\)
7360.2.a.s 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}-2q^{9}+4q^{11}+\cdots\)
7360.2.a.t 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{9}-2q^{11}+5q^{13}+\cdots\)
7360.2.a.u 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(1\) \(1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}-2q^{9}-q^{13}+q^{15}+\cdots\)
7360.2.a.v 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(1\) \(1\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}-2q^{9}-6q^{11}+\cdots\)
7360.2.a.w 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(2\) \(-1\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
7360.2.a.x 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(2\) \(1\) \(-5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}-5q^{7}+q^{9}+2q^{11}+\cdots\)
7360.2.a.y 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(2\) \(1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}+2q^{15}+\cdots\)
7360.2.a.z 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(2\) \(1\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+3q^{7}+q^{9}-6q^{11}+\cdots\)
7360.2.a.ba 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(3\) \(-1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{5}-2q^{7}+6q^{9}-q^{13}+\cdots\)
7360.2.a.bb 7360.a 1.a $1$ $58.770$ \(\Q\) None \(0\) \(3\) \(1\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}-2q^{7}+6q^{9}+3q^{13}+\cdots\)
7360.2.a.bc 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{13}) \) None \(0\) \(-3\) \(-2\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}-q^{5}+(2-\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
7360.2.a.bd 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{13}) \) None \(0\) \(-3\) \(2\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+q^{5}+(-2+\beta )q^{7}+\cdots\)
7360.2.a.be 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{7}) \) None \(0\) \(-2\) \(-2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(-1-\beta )q^{7}-2q^{9}+(-1+\cdots)q^{11}+\cdots\)
7360.2.a.bf 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(1+\beta )q^{7}-2q^{9}+(-1+\cdots)q^{11}+\cdots\)
7360.2.a.bg 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(1-\beta )q^{7}-2q^{9}+(1-\beta )q^{11}+\cdots\)
7360.2.a.bh 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(-2\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}+(1-\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
7360.2.a.bi 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}+(1-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
7360.2.a.bj 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}+2\beta q^{7}+(1+\beta )q^{9}+4q^{11}+\cdots\)
7360.2.a.bk 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{21}) \) None \(0\) \(-1\) \(2\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}+(-1+\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
7360.2.a.bl 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}+(1-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
7360.2.a.bm 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-2\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}-2\beta q^{7}+(1+\beta )q^{9}-4q^{11}+\cdots\)
7360.2.a.bn 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
7360.2.a.bo 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
7360.2.a.bp 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(2\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
7360.2.a.bq 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{21}) \) None \(0\) \(1\) \(2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+(1-\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
7360.2.a.br 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{7}) \) None \(0\) \(2\) \(-2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(1+\beta )q^{7}-2q^{9}+(1+\beta )q^{11}+\cdots\)
7360.2.a.bs 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(-1+\beta )q^{7}-2q^{9}+(-1+\cdots)q^{11}+\cdots\)
7360.2.a.bt 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(-1-\beta )q^{7}-2q^{9}+(1+\cdots)q^{11}+\cdots\)
7360.2.a.bu 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(-2\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}+(-2+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
7360.2.a.bv 7360.a 1.a $2$ $58.770$ \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(2\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+q^{5}+(2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
7360.2.a.bw 7360.a 1.a $3$ $58.770$ 3.3.229.1 None \(0\) \(-2\) \(-3\) \(7\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}-q^{5}+(2-\beta _{2})q^{7}+\cdots\)
7360.2.a.bx 7360.a 1.a $3$ $58.770$ 3.3.1573.1 None \(0\) \(-1\) \(-3\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(-1-\beta _{1})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
7360.2.a.by 7360.a 1.a $3$ $58.770$ 3.3.2597.1 None \(0\) \(-1\) \(-3\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(1-\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
7360.2.a.bz 7360.a 1.a $3$ $58.770$ 3.3.1101.1 None \(0\) \(-1\) \(3\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+(4+\cdots)q^{9}+\cdots\)
7360.2.a.ca 7360.a 1.a $3$ $58.770$ 3.3.621.1 None \(0\) \(0\) \(3\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(-1-\beta _{1})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
7360.2.a.cb 7360.a 1.a $3$ $58.770$ 3.3.621.1 None \(0\) \(0\) \(3\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(1+\beta _{1})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
7360.2.a.cc 7360.a 1.a $3$ $58.770$ 3.3.2597.1 None \(0\) \(1\) \(-3\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-1+\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
7360.2.a.cd 7360.a 1.a $3$ $58.770$ 3.3.1573.1 None \(0\) \(1\) \(-3\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(1+\beta _{1})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
7360.2.a.ce 7360.a 1.a $3$ $58.770$ 3.3.1101.1 None \(0\) \(1\) \(3\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
7360.2.a.cf 7360.a 1.a $3$ $58.770$ 3.3.229.1 None \(0\) \(2\) \(-3\) \(-7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}-q^{5}+(-2+\beta _{2})q^{7}+\cdots\)
7360.2.a.cg 7360.a 1.a $4$ $58.770$ 4.4.15317.1 None \(0\) \(-2\) \(-4\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}-q^{5}+(1+\beta _{3})q^{7}+\cdots\)
7360.2.a.ch 7360.a 1.a $4$ $58.770$ 4.4.21208.1 None \(0\) \(-1\) \(4\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+q^{5}+(1+\beta _{1})q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
7360.2.a.ci 7360.a 1.a $4$ $58.770$ 4.4.21208.1 None \(0\) \(1\) \(4\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+q^{5}+(-1-\beta _{1})q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
7360.2.a.cj 7360.a 1.a $4$ $58.770$ 4.4.15317.1 None \(0\) \(2\) \(-4\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}-q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
7360.2.a.ck 7360.a 1.a $5$ $58.770$ 5.5.406264.1 None \(0\) \(-3\) \(-5\) \(8\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}-q^{5}+(2-\beta _{1}+\beta _{4})q^{7}+\cdots\)
7360.2.a.cl 7360.a 1.a $5$ $58.770$ 5.5.876604.1 None \(0\) \(-1\) \(-5\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}-q^{5}+(\beta _{2}+\beta _{3}+\beta _{4})q^{7}+\cdots\)
7360.2.a.cm 7360.a 1.a $5$ $58.770$ 5.5.2255384.1 None \(0\) \(-1\) \(5\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
7360.2.a.cn 7360.a 1.a $5$ $58.770$ 5.5.1143052.1 None \(0\) \(-1\) \(5\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+q^{5}+(-1+2\beta _{1}-\beta _{2}+\beta _{4})q^{7}+\cdots\)
7360.2.a.co 7360.a 1.a $5$ $58.770$ 5.5.13955077.1 None \(0\) \(0\) \(5\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(2+\cdots)q^{9}+\cdots\)
7360.2.a.cp 7360.a 1.a $5$ $58.770$ 5.5.13955077.1 None \(0\) \(0\) \(5\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(\beta _{3}+\beta _{4})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
7360.2.a.cq 7360.a 1.a $5$ $58.770$ 5.5.876604.1 None \(0\) \(1\) \(-5\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}-q^{5}+(-\beta _{2}-\beta _{3}-\beta _{4})q^{7}+\cdots\)
7360.2.a.cr 7360.a 1.a $5$ $58.770$ 5.5.1143052.1 None \(0\) \(1\) \(5\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+q^{5}+(1-2\beta _{1}+\beta _{2}-\beta _{4})q^{7}+\cdots\)
7360.2.a.cs 7360.a 1.a $5$ $58.770$ 5.5.2255384.1 None \(0\) \(1\) \(5\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(\beta _{2}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
7360.2.a.ct 7360.a 1.a $5$ $58.770$ 5.5.406264.1 None \(0\) \(3\) \(-5\) \(-8\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}-q^{5}+(-2+\beta _{1}-\beta _{4})q^{7}+\cdots\)
7360.2.a.cu 7360.a 1.a $6$ $58.770$ 6.6.255601784.1 None \(0\) \(-5\) \(-6\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-q^{5}+(1+\beta _{3})q^{7}+\cdots\)
7360.2.a.cv 7360.a 1.a $6$ $58.770$ 6.6.255601784.1 None \(0\) \(5\) \(-6\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-q^{5}+(-1-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7360))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7360)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(736))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1472))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1840))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3680))\)\(^{\oplus 2}\)