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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 13
7605.2.a.a \(1\) \(60.726\) \(\Q\) None \(-2\) \(0\) \(1\) \(5\) \(-\) \(-\) \(+\) \(q-2q^{2}+2q^{4}+q^{5}+5q^{7}-2q^{10}+\cdots\)
7605.2.a.b \(1\) \(60.726\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{4}-q^{5}-4q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.c \(1\) \(60.726\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.d \(1\) \(60.726\) \(\Q\) None \(-1\) \(0\) \(-1\) \(2\) \(-\) \(+\) \(-\) \(q-q^{2}-q^{4}-q^{5}+2q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.e \(1\) \(60.726\) \(\Q\) None \(-1\) \(0\) \(-1\) \(4\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.f \(1\) \(60.726\) \(\Q\) None \(-1\) \(0\) \(-1\) \(4\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.g \(1\) \(60.726\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}-4q^{11}+\cdots\)
7605.2.a.h \(1\) \(60.726\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}+4q^{11}+\cdots\)
7605.2.a.i \(1\) \(60.726\) \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) \(-\) \(+\) \(-\) \(q-2q^{4}-q^{5}-3q^{7}-3q^{11}+4q^{16}+\cdots\)
7605.2.a.j \(1\) \(60.726\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(q-2q^{4}-q^{5}+q^{7}+3q^{11}+4q^{16}+\cdots\)
7605.2.a.k \(1\) \(60.726\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(q-2q^{4}-q^{5}+q^{7}+6q^{11}+4q^{16}+\cdots\)
7605.2.a.l \(1\) \(60.726\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(q-2q^{4}+q^{5}-q^{7}-6q^{11}+4q^{16}+\cdots\)
7605.2.a.m \(1\) \(60.726\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(+\) \(q-2q^{4}+q^{5}+q^{7}-3q^{11}+4q^{16}+\cdots\)
7605.2.a.n \(1\) \(60.726\) \(\Q\) None \(0\) \(0\) \(1\) \(3\) \(-\) \(-\) \(-\) \(q-2q^{4}+q^{5}+3q^{7}+3q^{11}+4q^{16}+\cdots\)
7605.2.a.o \(1\) \(60.726\) \(\Q\) None \(1\) \(0\) \(1\) \(-4\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{4}+q^{5}-4q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.p \(1\) \(60.726\) \(\Q\) None \(1\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.q \(1\) \(60.726\) \(\Q\) None \(1\) \(0\) \(1\) \(-2\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.r \(1\) \(60.726\) \(\Q\) None \(1\) \(0\) \(1\) \(4\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.s \(1\) \(60.726\) \(\Q\) None \(2\) \(0\) \(-1\) \(-5\) \(-\) \(+\) \(+\) \(q+2q^{2}+2q^{4}-q^{5}-5q^{7}-2q^{10}+\cdots\)
7605.2.a.t \(1\) \(60.726\) \(\Q\) None \(2\) \(0\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(q+2q^{2}+2q^{4}-q^{5}+q^{7}-2q^{10}+\cdots\)
7605.2.a.u \(1\) \(60.726\) \(\Q\) None \(2\) \(0\) \(1\) \(-3\) \(-\) \(-\) \(+\) \(q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots\)
7605.2.a.v \(1\) \(60.726\) \(\Q\) None \(2\) \(0\) \(1\) \(3\) \(-\) \(-\) \(+\) \(q+2q^{2}+2q^{4}+q^{5}+3q^{7}+2q^{10}+\cdots\)
7605.2.a.w \(2\) \(60.726\) \(\Q(\sqrt{13}) \) None \(-4\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{2}+2q^{4}+q^{5}-\beta q^{7}-2q^{10}+\cdots\)
7605.2.a.x \(2\) \(60.726\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(-4\) \(-\) \(-\) \(+\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-2+\cdots)q^{7}+\cdots\)
7605.2.a.y \(2\) \(60.726\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.z \(2\) \(60.726\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+q^{5}+\beta q^{7}+\cdots\)
7605.2.a.ba \(2\) \(60.726\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(-2\) \(4\) \(-\) \(+\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(3-2\beta )q^{7}+\cdots\)
7605.2.a.bb \(2\) \(60.726\) \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(-2\) \(2\) \(-\) \(+\) \(+\) \(q-\beta q^{2}+(1+\beta )q^{4}-q^{5}+q^{7}-3q^{8}+\cdots\)
7605.2.a.bc \(2\) \(60.726\) \(\Q(\sqrt{17}) \) None \(-1\) \(0\) \(-2\) \(-3\) \(-\) \(+\) \(-\) \(q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(-1-\beta )q^{7}+\cdots\)
7605.2.a.bd \(2\) \(60.726\) \(\Q(\sqrt{17}) \) None \(-1\) \(0\) \(-2\) \(5\) \(+\) \(+\) \(+\) \(q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(3-\beta )q^{7}+\cdots\)
7605.2.a.be \(2\) \(60.726\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(-4\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+q^{4}-q^{5}-2q^{7}-\beta q^{8}-\beta q^{10}+\cdots\)
7605.2.a.bf \(2\) \(60.726\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(2\) \(-4\) \(-\) \(-\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-3+2\beta )q^{7}+\cdots\)
7605.2.a.bg \(2\) \(60.726\) \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(2\) \(-2\) \(-\) \(-\) \(+\) \(q+\beta q^{2}+(1+\beta )q^{4}+q^{5}-q^{7}+3q^{8}+\cdots\)
7605.2.a.bh \(2\) \(60.726\) \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(2\) \(3\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(1+\beta )q^{7}+\cdots\)
7605.2.a.bi \(2\) \(60.726\) \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(2\) \(5\) \(+\) \(-\) \(+\) \(q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(3-\beta )q^{7}+\cdots\)
7605.2.a.bj \(2\) \(60.726\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}-q^{5}+\beta q^{7}+\cdots\)
7605.2.a.bk \(2\) \(60.726\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+q^{5}+(1-2\beta )q^{7}+\cdots\)
7605.2.a.bl \(2\) \(60.726\) \(\Q(\sqrt{13}) \) None \(4\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(q+2q^{2}+2q^{4}-q^{5}+\beta q^{7}-2q^{10}+\cdots\)
7605.2.a.bm \(3\) \(60.726\) \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(3\) \(0\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1}+\beta _{2})q^{2}+(4-\beta _{1})q^{4}+\cdots\)
7605.2.a.bn \(3\) \(60.726\) \(\Q(\zeta_{14})^+\) None \(-2\) \(0\) \(-3\) \(-4\) \(-\) \(+\) \(-\) \(q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
7605.2.a.bo \(3\) \(60.726\) \(\Q(\zeta_{14})^+\) None \(-1\) \(0\) \(-3\) \(-4\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bp \(3\) \(60.726\) \(\Q(\zeta_{14})^+\) None \(-1\) \(0\) \(3\) \(-12\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}-4q^{7}+(-1+\cdots)q^{8}+\cdots\)
7605.2.a.bq \(3\) \(60.726\) \(\Q(\zeta_{14})^+\) None \(-1\) \(0\) \(3\) \(-2\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.br \(3\) \(60.726\) \(\Q(\zeta_{14})^+\) None \(-1\) \(0\) \(3\) \(5\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
7605.2.a.bs \(3\) \(60.726\) 3.3.564.1 None \(-1\) \(0\) \(3\) \(2\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1+\beta _{2})q^{7}+\cdots\)
7605.2.a.bt \(3\) \(60.726\) 3.3.148.1 None \(0\) \(0\) \(-3\) \(5\) \(-\) \(+\) \(+\) \(q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)
7605.2.a.bu \(3\) \(60.726\) 3.3.148.1 None \(0\) \(0\) \(3\) \(-5\) \(-\) \(-\) \(+\) \(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.bv \(3\) \(60.726\) 3.3.756.1 None \(0\) \(0\) \(-3\) \(3\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bw \(3\) \(60.726\) 3.3.756.1 None \(0\) \(0\) \(3\) \(-3\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bx \(3\) \(60.726\) 3.3.316.1 None \(0\) \(0\) \(-3\) \(-1\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(3+\beta _{2})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots\)
7605.2.a.by \(3\) \(60.726\) \(\Q(\zeta_{14})^+\) None \(1\) \(0\) \(-3\) \(-5\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bz \(3\) \(60.726\) \(\Q(\zeta_{14})^+\) None \(1\) \(0\) \(-3\) \(2\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(1-\beta _{1})q^{7}+\cdots\)
7605.2.a.ca \(3\) \(60.726\) \(\Q(\zeta_{14})^+\) None \(1\) \(0\) \(-3\) \(12\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+4q^{7}+(1-2\beta _{1}+\cdots)q^{8}+\cdots\)
7605.2.a.cb \(3\) \(60.726\) \(\Q(\zeta_{14})^+\) None \(1\) \(0\) \(3\) \(4\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(1+\beta _{1})q^{7}+\cdots\)
7605.2.a.cc \(3\) \(60.726\) 3.3.564.1 None \(1\) \(0\) \(-3\) \(-2\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
7605.2.a.cd \(3\) \(60.726\) \(\Q(\zeta_{14})^+\) None \(2\) \(0\) \(3\) \(4\) \(-\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
7605.2.a.ce \(3\) \(60.726\) \(\Q(\zeta_{14})^+\) None \(3\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}-q^{5}+\cdots\)
7605.2.a.cf \(4\) \(60.726\) 4.4.4752.1 None \(-2\) \(0\) \(4\) \(10\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+(3+\beta _{2}+\cdots)q^{7}+\cdots\)
7605.2.a.cg \(4\) \(60.726\) 4.4.7488.1 None \(-2\) \(0\) \(-4\) \(6\) \(-\) \(+\) \(-\) \(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}-q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.ch \(4\) \(60.726\) 4.4.13824.1 None \(0\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
7605.2.a.ci \(4\) \(60.726\) 4.4.13824.1 None \(0\) \(0\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
7605.2.a.cj \(4\) \(60.726\) 4.4.4752.1 None \(2\) \(0\) \(-4\) \(-10\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+(-3+\cdots)q^{7}+\cdots\)
7605.2.a.ck \(4\) \(60.726\) 4.4.7488.1 None \(2\) \(0\) \(4\) \(-6\) \(-\) \(-\) \(-\) \(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.cl \(5\) \(60.726\) 5.5.3352656.1 None \(-2\) \(0\) \(-5\) \(-1\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-\beta _{4}q^{7}+\cdots\)
7605.2.a.cm \(5\) \(60.726\) 5.5.3352656.1 None \(-2\) \(0\) \(-5\) \(1\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{4}q^{7}+\cdots\)
7605.2.a.cn \(5\) \(60.726\) 5.5.3352656.1 None \(2\) \(0\) \(5\) \(-1\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-\beta _{4}q^{7}+\cdots\)
7605.2.a.co \(5\) \(60.726\) 5.5.3352656.1 None \(2\) \(0\) \(5\) \(1\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+\beta _{4}q^{7}+\cdots\)
7605.2.a.cp \(9\) \(60.726\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-3\) \(0\) \(-9\) \(7\) \(-\) \(+\) \(+\) \(q+(-\beta _{1}-\beta _{6})q^{2}+(2-\beta _{3}-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
7605.2.a.cq \(9\) \(60.726\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(0\) \(-9\) \(-10\) \(-\) \(+\) \(+\) \(q+\beta _{7}q^{2}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
7605.2.a.cr \(9\) \(60.726\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(0\) \(9\) \(10\) \(-\) \(-\) \(-\) \(q-\beta _{7}q^{2}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
7605.2.a.cs \(9\) \(60.726\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(3\) \(0\) \(9\) \(-7\) \(-\) \(-\) \(-\) \(q+(\beta _{1}+\beta _{6})q^{2}+(2-\beta _{3}-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
7605.2.a.ct \(10\) \(60.726\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(10\) \(0\) \(+\) \(-\) \(-\) \(q-\beta _{4}q^{2}+(1+\beta _{5})q^{4}+q^{5}+\beta _{9}q^{7}+\cdots\)
7605.2.a.cu \(10\) \(60.726\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(0\) \(-10\) \(0\) \(+\) \(+\) \(-\) \(q+\beta _{4}q^{2}+(1+\beta _{5})q^{4}-q^{5}+\beta _{9}q^{7}+\cdots\)
7605.2.a.cv \(12\) \(60.726\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(0\) \(12\) \(-12\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.cw \(12\) \(60.726\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(0\) \(12\) \(12\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}+q^{5}+(1+\cdots)q^{7}+\cdots\)
7605.2.a.cx \(12\) \(60.726\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(0\) \(-12\) \(-12\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.cy \(12\) \(60.726\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(0\) \(-12\) \(12\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)

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

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