Properties

Label 7616.2.a
Level $7616$
Weight $2$
Character orbit 7616.a
Rep. character $\chi_{7616}(1,\cdot)$
Character field $\Q$
Dimension $192$
Newform subspaces $58$
Sturm bound $2304$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 7616 = 2^{6} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7616.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 58 \)
Sturm bound: \(2304\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7616))\).

Total New Old
Modular forms 1176 192 984
Cusp forms 1129 192 937
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.

\(2\)\(7\)\(17\)FrickeDim
\(+\)\(+\)\(+\)$+$\(22\)
\(+\)\(+\)\(-\)$-$\(27\)
\(+\)\(-\)\(+\)$-$\(26\)
\(+\)\(-\)\(-\)$+$\(21\)
\(-\)\(+\)\(+\)$-$\(26\)
\(-\)\(+\)\(-\)$+$\(21\)
\(-\)\(-\)\(+\)$+$\(22\)
\(-\)\(-\)\(-\)$-$\(27\)
Plus space\(+\)\(86\)
Minus space\(-\)\(106\)

Trace form

\( 192 q + 192 q^{9} + O(q^{10}) \) \( 192 q + 192 q^{9} + 192 q^{25} + 16 q^{29} + 16 q^{37} - 96 q^{45} + 192 q^{49} - 80 q^{53} - 96 q^{69} + 16 q^{77} + 192 q^{81} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7616))\) 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 7 17
7616.2.a.a 7616.a 1.a $1$ $60.814$ \(\Q\) None \(0\) \(-2\) \(-4\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{5}+q^{7}+q^{9}+4q^{11}+\cdots\)
7616.2.a.b 7616.a 1.a $1$ $60.814$ \(\Q\) None \(0\) \(-2\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}-6q^{11}-6q^{13}+\cdots\)
7616.2.a.c 7616.a 1.a $1$ $60.814$ \(\Q\) None \(0\) \(-2\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
7616.2.a.d 7616.a 1.a $1$ $60.814$ \(\Q\) None \(0\) \(-2\) \(4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{5}-q^{7}+q^{9}-6q^{11}+\cdots\)
7616.2.a.e 7616.a 1.a $1$ $60.814$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-3q^{9}+2q^{13}+q^{17}+\cdots\)
7616.2.a.f 7616.a 1.a $1$ $60.814$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-3q^{9}+2q^{13}+q^{17}+\cdots\)
7616.2.a.g 7616.a 1.a $1$ $60.814$ \(\Q\) None \(0\) \(0\) \(2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-3q^{9}+2q^{11}-q^{17}+\cdots\)
7616.2.a.h 7616.a 1.a $1$ $60.814$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-3q^{9}-2q^{11}-q^{17}+\cdots\)
7616.2.a.i 7616.a 1.a $1$ $60.814$ \(\Q\) None \(0\) \(2\) \(-4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-4q^{5}-q^{7}+q^{9}-4q^{11}+\cdots\)
7616.2.a.j 7616.a 1.a $1$ $60.814$ \(\Q\) None \(0\) \(2\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
7616.2.a.k 7616.a 1.a $1$ $60.814$ \(\Q\) None \(0\) \(2\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{7}+q^{9}+6q^{11}-6q^{13}+\cdots\)
7616.2.a.l 7616.a 1.a $1$ $60.814$ \(\Q\) None \(0\) \(2\) \(4\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{5}+q^{7}+q^{9}+6q^{11}+\cdots\)
7616.2.a.m 7616.a 1.a $2$ $60.814$ \(\Q(\sqrt{13}) \) None \(0\) \(-3\) \(3\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(2-\beta )q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
7616.2.a.n 7616.a 1.a $2$ $60.814$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+\cdots\)
7616.2.a.o 7616.a 1.a $2$ $60.814$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(-1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{5}+q^{7}+\beta q^{9}+\cdots\)
7616.2.a.p 7616.a 1.a $2$ $60.814$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots\)
7616.2.a.q 7616.a 1.a $2$ $60.814$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{5}+q^{7}+\beta q^{9}+(-4+\cdots)q^{13}+\cdots\)
7616.2.a.r 7616.a 1.a $2$ $60.814$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(3\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1+\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots\)
7616.2.a.s 7616.a 1.a $2$ $60.814$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(3\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1+\beta )q^{5}-q^{7}+\beta q^{9}+(-2+\cdots)q^{11}+\cdots\)
7616.2.a.t 7616.a 1.a $2$ $60.814$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+\beta )q^{5}-q^{7}+\beta q^{9}+\cdots\)
7616.2.a.u 7616.a 1.a $2$ $60.814$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots\)
7616.2.a.v 7616.a 1.a $2$ $60.814$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{5}-q^{7}+\beta q^{9}+(-4+\cdots)q^{13}+\cdots\)
7616.2.a.w 7616.a 1.a $2$ $60.814$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(3\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1+\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots\)
7616.2.a.x 7616.a 1.a $2$ $60.814$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(3\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1+\beta )q^{5}+q^{7}+\beta q^{9}+(2+\cdots)q^{11}+\cdots\)
7616.2.a.y 7616.a 1.a $2$ $60.814$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1+\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
7616.2.a.z 7616.a 1.a $2$ $60.814$ \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(3\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2-\beta )q^{5}+q^{7}+(1+3\beta )q^{9}+\cdots\)
7616.2.a.ba 7616.a 1.a $3$ $60.814$ 3.3.229.1 None \(0\) \(-3\) \(-1\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+\beta _{2}q^{5}+q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
7616.2.a.bb 7616.a 1.a $3$ $60.814$ 3.3.229.1 None \(0\) \(-3\) \(5\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+(2+\beta _{2})q^{5}-q^{7}+\cdots\)
7616.2.a.bc 7616.a 1.a $3$ $60.814$ 3.3.229.1 None \(0\) \(-1\) \(-3\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
7616.2.a.bd 7616.a 1.a $3$ $60.814$ 3.3.1229.1 None \(0\) \(-1\) \(-3\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots\)
7616.2.a.be 7616.a 1.a $3$ $60.814$ 3.3.229.1 None \(0\) \(1\) \(-3\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}-q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
7616.2.a.bf 7616.a 1.a $3$ $60.814$ 3.3.1229.1 None \(0\) \(1\) \(-3\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots\)
7616.2.a.bg 7616.a 1.a $3$ $60.814$ 3.3.229.1 None \(0\) \(3\) \(-1\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}-q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
7616.2.a.bh 7616.a 1.a $3$ $60.814$ 3.3.229.1 None \(0\) \(3\) \(5\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+(2+\beta _{2})q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
7616.2.a.bi 7616.a 1.a $4$ $60.814$ 4.4.13448.1 None \(0\) \(-3\) \(-5\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{3}+(-1+\beta _{2})q^{5}+q^{7}+\cdots\)
7616.2.a.bj 7616.a 1.a $4$ $60.814$ 4.4.5225.1 None \(0\) \(-3\) \(1\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}-q^{7}+\cdots\)
7616.2.a.bk 7616.a 1.a $4$ $60.814$ 4.4.9301.1 None \(0\) \(-2\) \(-2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+\beta _{2}q^{5}+q^{7}+(2-\beta _{3})q^{9}+\cdots\)
7616.2.a.bl 7616.a 1.a $4$ $60.814$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(4\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{1})q^{5}-q^{7}+\beta _{2}q^{9}+\cdots\)
7616.2.a.bm 7616.a 1.a $4$ $60.814$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(4\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{1})q^{5}+q^{7}+\beta _{2}q^{9}+\cdots\)
7616.2.a.bn 7616.a 1.a $4$ $60.814$ 4.4.9301.1 None \(0\) \(2\) \(-2\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+\beta _{2}q^{5}-q^{7}+(2-\beta _{3})q^{9}+\cdots\)
7616.2.a.bo 7616.a 1.a $4$ $60.814$ 4.4.13448.1 None \(0\) \(3\) \(-5\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(-1+\beta _{3})q^{5}-q^{7}+\cdots\)
7616.2.a.bp 7616.a 1.a $4$ $60.814$ 4.4.5225.1 None \(0\) \(3\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots\)
7616.2.a.bq 7616.a 1.a $5$ $60.814$ 5.5.453749.1 None \(0\) \(-2\) \(0\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
7616.2.a.br 7616.a 1.a $5$ $60.814$ 5.5.804272.1 None \(0\) \(0\) \(2\) \(-5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}-q^{7}+\cdots\)
7616.2.a.bs 7616.a 1.a $5$ $60.814$ 5.5.804272.1 None \(0\) \(0\) \(2\) \(5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+q^{7}+\cdots\)
7616.2.a.bt 7616.a 1.a $5$ $60.814$ 5.5.453749.1 None \(0\) \(2\) \(0\) \(-5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}-q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
7616.2.a.bu 7616.a 1.a $6$ $60.814$ 6.6.109859312.1 None \(0\) \(-4\) \(-4\) \(6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{5})q^{3}+(-1+\beta _{1})q^{5}+q^{7}+\cdots\)
7616.2.a.bv 7616.a 1.a $6$ $60.814$ 6.6.147697840.1 None \(0\) \(-4\) \(4\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(1+\beta _{5})q^{5}-q^{7}+\cdots\)
7616.2.a.bw 7616.a 1.a $6$ $60.814$ 6.6.4022000.1 None \(0\) \(-2\) \(-2\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+\beta _{1}q^{5}+q^{7}+(1-\beta _{5})q^{9}+\cdots\)
7616.2.a.bx 7616.a 1.a $6$ $60.814$ 6.6.80686992.1 None \(0\) \(-2\) \(6\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{4})q^{5}-q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
7616.2.a.by 7616.a 1.a $6$ $60.814$ 6.6.93059344.1 None \(0\) \(0\) \(-4\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{5})q^{5}-q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
7616.2.a.bz 7616.a 1.a $6$ $60.814$ 6.6.93059344.1 None \(0\) \(0\) \(-4\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1+\beta _{5})q^{5}+q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
7616.2.a.ca 7616.a 1.a $6$ $60.814$ 6.6.4022000.1 None \(0\) \(2\) \(-2\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+\beta _{1}q^{5}-q^{7}+(1-\beta _{5})q^{9}+\cdots\)
7616.2.a.cb 7616.a 1.a $6$ $60.814$ 6.6.80686992.1 None \(0\) \(2\) \(6\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{4})q^{5}+q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
7616.2.a.cc 7616.a 1.a $6$ $60.814$ 6.6.109859312.1 None \(0\) \(4\) \(-4\) \(-6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{5})q^{3}+(-1+\beta _{1})q^{5}-q^{7}+\cdots\)
7616.2.a.cd 7616.a 1.a $6$ $60.814$ 6.6.147697840.1 None \(0\) \(4\) \(4\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1+\beta _{5})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots\)
7616.2.a.ce 7616.a 1.a $8$ $60.814$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-2\) \(-6\) \(8\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{3}+(-1-\beta _{5})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
7616.2.a.cf 7616.a 1.a $8$ $60.814$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(2\) \(-6\) \(-8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{3}+(-1-\beta _{5})q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7616))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7616)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(544))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(952))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1088))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1904))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3808))\)\(^{\oplus 2}\)