Properties

Label 7942.2.a
Level $7942$
Weight $2$
Character orbit 7942.a
Rep. character $\chi_{7942}(1,\cdot)$
Character field $\Q$
Dimension $285$
Newform subspaces $56$
Sturm bound $2280$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7942.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 56 \)
Sturm bound: \(2280\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7942))\).

Total New Old
Modular forms 1180 285 895
Cusp forms 1101 285 816
Eisenstein series 79 0 79

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

\(2\)\(11\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(35\)
\(+\)\(+\)\(-\)\(-\)\(37\)
\(+\)\(-\)\(+\)\(-\)\(34\)
\(+\)\(-\)\(-\)\(+\)\(37\)
\(-\)\(+\)\(+\)\(-\)\(39\)
\(-\)\(+\)\(-\)\(+\)\(32\)
\(-\)\(-\)\(+\)\(+\)\(30\)
\(-\)\(-\)\(-\)\(-\)\(41\)
Plus space\(+\)\(134\)
Minus space\(-\)\(151\)

Trace form

\( 285 q - q^{2} + 285 q^{4} - 6 q^{5} - 4 q^{6} + 8 q^{7} - q^{8} + 281 q^{9} + O(q^{10}) \) \( 285 q - q^{2} + 285 q^{4} - 6 q^{5} - 4 q^{6} + 8 q^{7} - q^{8} + 281 q^{9} - 6 q^{10} - q^{11} + 2 q^{13} + 16 q^{15} + 285 q^{16} + 14 q^{17} + 3 q^{18} - 6 q^{20} + 16 q^{21} + q^{22} + 20 q^{23} - 4 q^{24} + 287 q^{25} - 10 q^{26} + 8 q^{28} - 6 q^{29} - 8 q^{30} + 4 q^{31} - q^{32} - 2 q^{34} + 8 q^{35} + 281 q^{36} + 14 q^{37} + 56 q^{39} - 6 q^{40} - 2 q^{41} + 20 q^{43} - q^{44} + 18 q^{45} - 16 q^{46} + 28 q^{47} + 285 q^{49} + q^{50} + 32 q^{51} + 2 q^{52} + 14 q^{53} + 8 q^{54} - 6 q^{55} - 18 q^{58} + 8 q^{59} + 16 q^{60} - 6 q^{61} + 48 q^{63} + 285 q^{64} - 12 q^{65} - 4 q^{66} - 8 q^{67} + 14 q^{68} - 16 q^{69} + 8 q^{70} + 12 q^{71} + 3 q^{72} + 14 q^{73} + 2 q^{74} - 32 q^{75} - 8 q^{77} + 24 q^{78} + 16 q^{79} - 6 q^{80} + 309 q^{81} - 18 q^{82} - 4 q^{83} + 16 q^{84} - 52 q^{85} + 4 q^{86} + 56 q^{87} + q^{88} + 26 q^{89} + 10 q^{90} + 16 q^{91} + 20 q^{92} + 8 q^{93} - 4 q^{96} - 38 q^{97} + 23 q^{98} - 13 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7942))\) 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 11 19
7942.2.a.a 7942.a 1.a $1$ $63.417$ \(\Q\) None \(-1\) \(-3\) \(-2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}-2q^{5}+3q^{6}+q^{7}+\cdots\)
7942.2.a.b 7942.a 1.a $1$ $63.417$ \(\Q\) None \(-1\) \(-2\) \(-3\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}-q^{7}+\cdots\)
7942.2.a.c 7942.a 1.a $1$ $63.417$ \(\Q\) None \(-1\) \(-2\) \(1\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-3q^{7}+\cdots\)
7942.2.a.d 7942.a 1.a $1$ $63.417$ \(\Q\) None \(-1\) \(0\) \(-4\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{5}-4q^{7}-q^{8}-3q^{9}+\cdots\)
7942.2.a.e 7942.a 1.a $1$ $63.417$ \(\Q\) None \(-1\) \(0\) \(-3\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}+3q^{7}-q^{8}-3q^{9}+\cdots\)
7942.2.a.f 7942.a 1.a $1$ $63.417$ \(\Q\) None \(-1\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
7942.2.a.g 7942.a 1.a $1$ $63.417$ \(\Q\) None \(-1\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}+2q^{7}-q^{8}-3q^{9}+\cdots\)
7942.2.a.h 7942.a 1.a $1$ $63.417$ \(\Q\) None \(-1\) \(1\) \(-4\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
7942.2.a.i 7942.a 1.a $1$ $63.417$ \(\Q\) None \(-1\) \(1\) \(-2\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-3q^{7}+\cdots\)
7942.2.a.j 7942.a 1.a $1$ $63.417$ \(\Q\) None \(-1\) \(2\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}+2q^{7}-q^{8}+\cdots\)
7942.2.a.k 7942.a 1.a $1$ $63.417$ \(\Q\) None \(-1\) \(2\) \(2\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}+2q^{7}+\cdots\)
7942.2.a.l 7942.a 1.a $1$ $63.417$ \(\Q\) None \(1\) \(-2\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+2q^{7}+q^{8}+\cdots\)
7942.2.a.m 7942.a 1.a $1$ $63.417$ \(\Q\) None \(1\) \(-2\) \(2\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}+2q^{5}-2q^{6}+2q^{7}+\cdots\)
7942.2.a.n 7942.a 1.a $1$ $63.417$ \(\Q\) None \(1\) \(-1\) \(-4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
7942.2.a.o 7942.a 1.a $1$ $63.417$ \(\Q\) None \(1\) \(0\) \(-4\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{5}-4q^{7}+q^{8}-3q^{9}+\cdots\)
7942.2.a.p 7942.a 1.a $1$ $63.417$ \(\Q\) None \(1\) \(0\) \(-3\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+3q^{7}+q^{8}-3q^{9}+\cdots\)
7942.2.a.q 7942.a 1.a $1$ $63.417$ \(\Q\) None \(1\) \(0\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
7942.2.a.r 7942.a 1.a $1$ $63.417$ \(\Q\) None \(1\) \(2\) \(-3\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}-3q^{5}+2q^{6}-q^{7}+\cdots\)
7942.2.a.s 7942.a 1.a $1$ $63.417$ \(\Q\) None \(1\) \(2\) \(1\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}-3q^{7}+\cdots\)
7942.2.a.t 7942.a 1.a $2$ $63.417$ \(\Q(\sqrt{5}) \) None \(-2\) \(-3\) \(-3\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
7942.2.a.u 7942.a 1.a $2$ $63.417$ \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+(2-3\beta )q^{5}+\beta q^{6}+\cdots\)
7942.2.a.v 7942.a 1.a $2$ $63.417$ \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+\beta q^{7}-q^{8}+\cdots\)
7942.2.a.w 7942.a 1.a $2$ $63.417$ \(\Q(\sqrt{21}) \) None \(-2\) \(1\) \(3\) \(-5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+(2-\beta )q^{5}-\beta q^{6}+\cdots\)
7942.2.a.x 7942.a 1.a $2$ $63.417$ \(\Q(\sqrt{17}) \) None \(2\) \(-1\) \(4\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}+2q^{5}-\beta q^{6}+(2+\cdots)q^{7}+\cdots\)
7942.2.a.y 7942.a 1.a $2$ $63.417$ \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}-\beta q^{7}+q^{8}+\cdots\)
7942.2.a.z 7942.a 1.a $2$ $63.417$ \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+(2-3\beta )q^{5}+\beta q^{6}+\cdots\)
7942.2.a.ba 7942.a 1.a $2$ $63.417$ \(\Q(\sqrt{5}) \) None \(2\) \(3\) \(-3\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
7942.2.a.bb 7942.a 1.a $2$ $63.417$ \(\Q(\sqrt{13}) \) None \(2\) \(3\) \(-1\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots\)
7942.2.a.bc 7942.a 1.a $3$ $63.417$ 3.3.469.1 None \(-3\) \(-1\) \(5\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(2-\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots\)
7942.2.a.bd 7942.a 1.a $3$ $63.417$ 3.3.1940.1 None \(-3\) \(0\) \(6\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+2q^{5}+\beta _{1}q^{6}+\cdots\)
7942.2.a.be 7942.a 1.a $3$ $63.417$ 3.3.148.1 None \(-3\) \(2\) \(2\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+2\beta _{1}q^{5}+\cdots\)
7942.2.a.bf 7942.a 1.a $3$ $63.417$ 3.3.469.1 None \(-3\) \(4\) \(1\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{1})q^{3}+q^{4}-\beta _{2}q^{5}+(-1+\cdots)q^{6}+\cdots\)
7942.2.a.bg 7942.a 1.a $3$ $63.417$ 3.3.469.1 None \(3\) \(-4\) \(1\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}-\beta _{2}q^{5}+\cdots\)
7942.2.a.bh 7942.a 1.a $3$ $63.417$ 3.3.148.1 None \(3\) \(-2\) \(2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+2\beta _{1}q^{5}+\cdots\)
7942.2.a.bi 7942.a 1.a $3$ $63.417$ 3.3.621.1 None \(3\) \(0\) \(-3\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots\)
7942.2.a.bj 7942.a 1.a $3$ $63.417$ 3.3.1940.1 None \(3\) \(0\) \(6\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+2q^{5}+\beta _{1}q^{6}+\cdots\)
7942.2.a.bk 7942.a 1.a $6$ $63.417$ 6.6.485125.1 None \(-6\) \(5\) \(4\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{2}-\beta _{4}+\beta _{5})q^{3}+q^{4}+\cdots\)
7942.2.a.bl 7942.a 1.a $6$ $63.417$ 6.6.485125.1 None \(6\) \(-5\) \(4\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{2}+\beta _{4}-\beta _{5})q^{3}+q^{4}+\cdots\)
7942.2.a.bm 7942.a 1.a $8$ $63.417$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(-4\) \(1\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1}-\beta _{7})q^{3}+q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
7942.2.a.bn 7942.a 1.a $8$ $63.417$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(-1\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
7942.2.a.bo 7942.a 1.a $8$ $63.417$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(5\) \(1\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
7942.2.a.bp 7942.a 1.a $8$ $63.417$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-5\) \(1\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
7942.2.a.bq 7942.a 1.a $8$ $63.417$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(1\) \(-3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
7942.2.a.br 7942.a 1.a $8$ $63.417$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(4\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1}+\beta _{7})q^{3}+q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
7942.2.a.bs 7942.a 1.a $12$ $63.417$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(3\) \(-9\) \(-12\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{9})q^{5}+\cdots\)
7942.2.a.bt 7942.a 1.a $12$ $63.417$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(3\) \(-9\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
7942.2.a.bu 7942.a 1.a $12$ $63.417$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(6\) \(-6\) \(-6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+\beta _{11}q^{5}+\cdots\)
7942.2.a.bv 7942.a 1.a $12$ $63.417$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(-6\) \(-6\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+\beta _{11}q^{5}+\cdots\)
7942.2.a.bw 7942.a 1.a $12$ $63.417$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(-3\) \(-9\) \(-12\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{9})q^{5}+\cdots\)
7942.2.a.bx 7942.a 1.a $12$ $63.417$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(-3\) \(-9\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
7942.2.a.by 7942.a 1.a $15$ $63.417$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-15\) \(-3\) \(9\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1+\beta _{8})q^{5}+\beta _{1}q^{6}+\cdots\)
7942.2.a.bz 7942.a 1.a $15$ $63.417$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-15\) \(-3\) \(9\) \(12\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1+\beta _{12})q^{5}+\cdots\)
7942.2.a.ca 7942.a 1.a $15$ $63.417$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(3\) \(9\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{8})q^{5}+\beta _{1}q^{6}+\cdots\)
7942.2.a.cb 7942.a 1.a $15$ $63.417$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(3\) \(9\) \(12\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{12})q^{5}+\cdots\)
7942.2.a.cc 7942.a 1.a $16$ $63.417$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(-10\) \(0\) \(6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}-\beta _{5}q^{5}+\cdots\)
7942.2.a.cd 7942.a 1.a $16$ $63.417$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(10\) \(0\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{5}q^{5}+(1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7942))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7942)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(418))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3971))\)\(^{\oplus 2}\)