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Properties

Label 5586.2.a
Level $5586$
Weight $2$
Character orbit 5586.a
Rep. character $\chi_{5586}(1,\cdot)$
Character field $\Q$
Dimension $124$
Newform subspaces $58$
Sturm bound $2240$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5586.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 58 \)
Sturm bound: \(2240\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5586))\).

Total New Old
Modular forms 1152 124 1028
Cusp forms 1089 124 965
Eisenstein series 63 0 63

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

\(2\)\(3\)\(7\)\(19\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(7\)
\(+\)\(+\)\(+\)\(-\)$-$\(10\)
\(+\)\(+\)\(-\)\(+\)$-$\(8\)
\(+\)\(+\)\(-\)\(-\)$+$\(5\)
\(+\)\(-\)\(+\)\(+\)$-$\(8\)
\(+\)\(-\)\(+\)\(-\)$+$\(7\)
\(+\)\(-\)\(-\)\(+\)$+$\(8\)
\(+\)\(-\)\(-\)\(-\)$-$\(8\)
\(-\)\(+\)\(+\)\(+\)$-$\(10\)
\(-\)\(+\)\(+\)\(-\)$+$\(5\)
\(-\)\(+\)\(-\)\(+\)$+$\(7\)
\(-\)\(+\)\(-\)\(-\)$-$\(10\)
\(-\)\(-\)\(+\)\(+\)$+$\(5\)
\(-\)\(-\)\(+\)\(-\)$-$\(12\)
\(-\)\(-\)\(-\)\(+\)$-$\(10\)
\(-\)\(-\)\(-\)\(-\)$+$\(4\)
Plus space\(+\)\(48\)
Minus space\(-\)\(76\)

Trace form

\( 124 q + 2 q^{2} + 124 q^{4} - 2 q^{6} + 2 q^{8} + 124 q^{9} + O(q^{10}) \) \( 124 q + 2 q^{2} + 124 q^{4} - 2 q^{6} + 2 q^{8} + 124 q^{9} + 4 q^{11} + 12 q^{13} - 4 q^{15} + 124 q^{16} + 8 q^{17} + 2 q^{18} - 2 q^{19} - 4 q^{22} + 4 q^{23} - 2 q^{24} + 124 q^{25} + 12 q^{26} - 4 q^{29} + 4 q^{30} + 4 q^{31} + 2 q^{32} + 4 q^{33} + 20 q^{34} + 124 q^{36} - 12 q^{37} + 8 q^{39} - 12 q^{41} + 8 q^{43} + 4 q^{44} - 28 q^{47} + 78 q^{50} - 16 q^{51} + 12 q^{52} + 68 q^{53} - 2 q^{54} - 48 q^{55} + 2 q^{57} + 64 q^{58} - 4 q^{60} + 16 q^{61} - 16 q^{62} + 124 q^{64} + 40 q^{65} + 4 q^{66} - 16 q^{67} + 8 q^{68} - 8 q^{69} - 16 q^{71} + 2 q^{72} + 68 q^{74} - 2 q^{76} - 8 q^{78} + 36 q^{79} + 124 q^{81} - 32 q^{82} - 20 q^{83} + 48 q^{85} - 24 q^{86} - 12 q^{87} - 4 q^{88} + 12 q^{89} + 4 q^{92} + 24 q^{93} + 40 q^{94} - 4 q^{95} - 2 q^{96} - 16 q^{97} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5586))\) 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 3 7 19
5586.2.a.a 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(-4\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.b 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.c 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.d 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.e 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.f 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.g 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.h 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.i 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.j 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.k 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.l 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(-3\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.m 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.n 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.o 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.p 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.q 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.r 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.s 5586.a 1.a $1$ $44.604$ \(\Q\) None \(-1\) \(1\) \(1\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.t 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.u 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
5586.2.a.v 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.w 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(-1\) \(2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.x 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(-1\) \(4\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.y 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.z 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.ba 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.bb 5586.a 1.a $1$ $44.604$ \(\Q\) None \(1\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.bc 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{7}) \) None \(-2\) \(-2\) \(-2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.bd 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.be 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bf 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{7}) \) None \(-2\) \(2\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bg 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-6\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-3+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bh 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bi 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bj 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
5586.2.a.bk 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{7}) \) None \(2\) \(-2\) \(2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bl 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(4\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bm 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(-4\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.bn 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{7}) \) None \(2\) \(2\) \(-2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.bo 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
5586.2.a.bp 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.bq 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.br 5586.a 1.a $2$ $44.604$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(6\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(3+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.bs 5586.a 1.a $3$ $44.604$ 3.3.404.1 None \(-3\) \(-3\) \(1\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.bt 5586.a 1.a $3$ $44.604$ 3.3.404.1 None \(-3\) \(3\) \(-1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.bu 5586.a 1.a $3$ $44.604$ 3.3.404.1 None \(3\) \(-3\) \(5\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(2-\beta _{1})q^{5}-q^{6}+\cdots\)
5586.2.a.bv 5586.a 1.a $3$ $44.604$ 3.3.404.1 None \(3\) \(3\) \(-5\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-2+\beta _{1})q^{5}+q^{6}+\cdots\)
5586.2.a.bw 5586.a 1.a $4$ $44.604$ 4.4.29268.1 None \(-4\) \(-4\) \(0\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.bx 5586.a 1.a $4$ $44.604$ 4.4.4352.1 None \(-4\) \(-4\) \(4\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1+\beta _{3})q^{5}+q^{6}+\cdots\)
5586.2.a.by 5586.a 1.a $4$ $44.604$ 4.4.4352.1 None \(-4\) \(4\) \(-4\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1-\beta _{3})q^{5}-q^{6}+\cdots\)
5586.2.a.bz 5586.a 1.a $4$ $44.604$ 4.4.29268.1 None \(-4\) \(4\) \(0\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.ca 5586.a 1.a $4$ $44.604$ 4.4.202932.1 None \(4\) \(-4\) \(-2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.cb 5586.a 1.a $4$ $44.604$ 4.4.202932.1 None \(4\) \(4\) \(2\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.cc 5586.a 1.a $6$ $44.604$ 6.6.207085568.1 None \(-6\) \(-6\) \(0\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{5}q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.cd 5586.a 1.a $6$ $44.604$ 6.6.207085568.1 None \(-6\) \(6\) \(0\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta _{5}q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.ce 5586.a 1.a $8$ $44.604$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-8\) \(-4\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta _{7}q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.cf 5586.a 1.a $8$ $44.604$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(8\) \(4\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta _{7}q^{5}+q^{6}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5586))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5586)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(798))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(931))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1862))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2793))\)\(^{\oplus 2}\)