Properties

Label 6498.2.a
Level $6498$
Weight $2$
Character orbit 6498.a
Rep. character $\chi_{6498}(1,\cdot)$
Character field $\Q$
Dimension $143$
Newform subspaces $59$
Sturm bound $2280$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 6498 = 2 \cdot 3^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6498.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 59 \)
Sturm bound: \(2280\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6498))\).

Total New Old
Modular forms 1220 143 1077
Cusp forms 1061 143 918
Eisenstein series 159 0 159

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

\(2\)\(3\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(17\)
\(+\)\(+\)\(-\)\(-\)\(12\)
\(+\)\(-\)\(+\)\(-\)\(22\)
\(+\)\(-\)\(-\)\(+\)\(20\)
\(-\)\(+\)\(+\)\(-\)\(17\)
\(-\)\(+\)\(-\)\(+\)\(12\)
\(-\)\(-\)\(+\)\(+\)\(18\)
\(-\)\(-\)\(-\)\(-\)\(25\)
Plus space\(+\)\(67\)
Minus space\(-\)\(76\)

Trace form

\( 143 q + q^{2} + 143 q^{4} - 4 q^{5} - 4 q^{7} + q^{8} + O(q^{10}) \) \( 143 q + q^{2} + 143 q^{4} - 4 q^{5} - 4 q^{7} + q^{8} - 2 q^{10} - 6 q^{11} + 6 q^{13} - 4 q^{14} + 143 q^{16} + 2 q^{17} - 4 q^{20} - 4 q^{22} - 12 q^{23} + 155 q^{25} - 8 q^{26} - 4 q^{28} + 2 q^{29} + 4 q^{31} + q^{32} - 2 q^{34} - 16 q^{35} + 18 q^{37} - 2 q^{40} + 18 q^{41} - 10 q^{43} - 6 q^{44} - 4 q^{46} + 24 q^{47} + 155 q^{49} + 15 q^{50} + 6 q^{52} - 6 q^{53} + 4 q^{55} - 4 q^{56} + 12 q^{58} + 28 q^{59} + 12 q^{61} - 4 q^{62} + 143 q^{64} + 8 q^{65} - 4 q^{67} + 2 q^{68} + 12 q^{70} - 12 q^{71} - 18 q^{73} + 16 q^{74} + 24 q^{77} - 4 q^{79} - 4 q^{80} + 10 q^{82} - 22 q^{83} + 20 q^{85} + 8 q^{86} - 4 q^{88} - 26 q^{89} - 8 q^{91} - 12 q^{92} + 8 q^{94} + 2 q^{97} + q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6498))\) 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 19
6498.2.a.a 6498.a 1.a $1$ $51.887$ \(\Q\) None \(-1\) \(0\) \(-2\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-3q^{7}-q^{8}+2q^{10}+\cdots\)
6498.2.a.b 6498.a 1.a $1$ $51.887$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-4q^{11}+\cdots\)
6498.2.a.c 6498.a 1.a $1$ $51.887$ \(\Q\) None \(-1\) \(0\) \(-2\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+3q^{7}-q^{8}+2q^{10}+\cdots\)
6498.2.a.d 6498.a 1.a $1$ $51.887$ \(\Q\) None \(-1\) \(0\) \(-2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+4q^{7}-q^{8}+2q^{10}+\cdots\)
6498.2.a.e 6498.a 1.a $1$ $51.887$ \(\Q\) None \(-1\) \(0\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{7}-q^{8}-3q^{11}-2q^{13}+\cdots\)
6498.2.a.f 6498.a 1.a $1$ $51.887$ \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}-5q^{13}+\cdots\)
6498.2.a.g 6498.a 1.a $1$ $51.887$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}+2q^{11}+3q^{13}+\cdots\)
6498.2.a.h 6498.a 1.a $1$ $51.887$ \(\Q\) None \(-1\) \(0\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+4q^{7}-q^{8}-4q^{11}-4q^{14}+\cdots\)
6498.2.a.i 6498.a 1.a $1$ $51.887$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+2q^{11}+\cdots\)
6498.2.a.j 6498.a 1.a $1$ $51.887$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+4q^{11}+\cdots\)
6498.2.a.k 6498.a 1.a $1$ $51.887$ \(\Q\) None \(-1\) \(0\) \(2\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}+3q^{7}-q^{8}-2q^{10}+\cdots\)
6498.2.a.l 6498.a 1.a $1$ $51.887$ \(\Q\) None \(-1\) \(0\) \(4\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+4q^{5}-3q^{7}-q^{8}-4q^{10}+\cdots\)
6498.2.a.m 6498.a 1.a $1$ $51.887$ \(\Q\) None \(1\) \(0\) \(-2\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}-3q^{7}+q^{8}-2q^{10}+\cdots\)
6498.2.a.n 6498.a 1.a $1$ $51.887$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-4q^{11}+\cdots\)
6498.2.a.o 6498.a 1.a $1$ $51.887$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-2q^{11}+\cdots\)
6498.2.a.p 6498.a 1.a $1$ $51.887$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+4q^{11}+\cdots\)
6498.2.a.q 6498.a 1.a $1$ $51.887$ \(\Q\) None \(1\) \(0\) \(-2\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+3q^{7}+q^{8}-2q^{10}+\cdots\)
6498.2.a.r 6498.a 1.a $1$ $51.887$ \(\Q\) None \(1\) \(0\) \(-2\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+4q^{7}+q^{8}-2q^{10}+\cdots\)
6498.2.a.s 6498.a 1.a $1$ $51.887$ \(\Q\) None \(1\) \(0\) \(0\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{7}+q^{8}-3q^{11}+2q^{13}+\cdots\)
6498.2.a.t 6498.a 1.a $1$ $51.887$ \(\Q\) None \(1\) \(0\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{7}+q^{8}+4q^{13}-4q^{14}+\cdots\)
6498.2.a.u 6498.a 1.a $1$ $51.887$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}-3q^{13}+\cdots\)
6498.2.a.v 6498.a 1.a $1$ $51.887$ \(\Q\) None \(1\) \(0\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+4q^{11}+\cdots\)
6498.2.a.w 6498.a 1.a $1$ $51.887$ \(\Q\) None \(1\) \(0\) \(2\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+3q^{7}+q^{8}+2q^{10}+\cdots\)
6498.2.a.x 6498.a 1.a $1$ $51.887$ \(\Q\) None \(1\) \(0\) \(4\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{5}-3q^{7}+q^{8}+4q^{10}+\cdots\)
6498.2.a.y 6498.a 1.a $1$ $51.887$ \(\Q\) None \(1\) \(0\) \(4\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{5}+3q^{7}+q^{8}+4q^{10}+\cdots\)
6498.2.a.z 6498.a 1.a $2$ $51.887$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-5\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-2-\beta )q^{5}+(2-\beta )q^{7}+\cdots\)
6498.2.a.ba 6498.a 1.a $2$ $51.887$ \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(-2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta )q^{5}+(1+\beta )q^{7}+\cdots\)
6498.2.a.bb 6498.a 1.a $2$ $51.887$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-1\) \(-5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta q^{5}+(-2-\beta )q^{7}-q^{8}+\cdots\)
6498.2.a.bc 6498.a 1.a $2$ $51.887$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(1\) \(-5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}+(-2-\beta )q^{7}-q^{8}+\cdots\)
6498.2.a.bd 6498.a 1.a $2$ $51.887$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+4q^{11}+\cdots\)
6498.2.a.be 6498.a 1.a $2$ $51.887$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(5\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(3-\beta )q^{5}+(-2+2\beta )q^{7}+\cdots\)
6498.2.a.bf 6498.a 1.a $2$ $51.887$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-5\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-2-\beta )q^{5}+(2-\beta )q^{7}+\cdots\)
6498.2.a.bg 6498.a 1.a $2$ $51.887$ \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(-2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta )q^{5}+(1+\beta )q^{7}+\cdots\)
6498.2.a.bh 6498.a 1.a $2$ $51.887$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-1\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-\beta q^{5}+(-2-\beta )q^{7}+q^{8}+\cdots\)
6498.2.a.bi 6498.a 1.a $2$ $51.887$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(1\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+(-2-\beta )q^{7}+q^{8}+\cdots\)
6498.2.a.bj 6498.a 1.a $2$ $51.887$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+4q^{11}+\cdots\)
6498.2.a.bk 6498.a 1.a $2$ $51.887$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(5\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(3-\beta )q^{5}+(-2+2\beta )q^{7}+\cdots\)
6498.2.a.bl 6498.a 1.a $3$ $51.887$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(-6\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+(2-2\beta _{1})q^{7}-q^{8}+\cdots\)
6498.2.a.bm 6498.a 1.a $3$ $51.887$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(0\) \(-9\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+(-3+\cdots)q^{7}+\cdots\)
6498.2.a.bn 6498.a 1.a $3$ $51.887$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(0\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-2\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
6498.2.a.bo 6498.a 1.a $3$ $51.887$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(6\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(2+\beta _{1})q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots\)
6498.2.a.bp 6498.a 1.a $3$ $51.887$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(6\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(2-\beta _{1})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)
6498.2.a.bq 6498.a 1.a $3$ $51.887$ \(\Q(\zeta_{18})^+\) None \(3\) \(0\) \(-6\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+(2-2\beta _{1})q^{7}+q^{8}+\cdots\)
6498.2.a.br 6498.a 1.a $3$ $51.887$ \(\Q(\zeta_{18})^+\) None \(3\) \(0\) \(0\) \(-9\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+(-3+\cdots)q^{7}+\cdots\)
6498.2.a.bs 6498.a 1.a $3$ $51.887$ \(\Q(\zeta_{18})^+\) None \(3\) \(0\) \(0\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-2\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
6498.2.a.bt 6498.a 1.a $3$ $51.887$ \(\Q(\zeta_{18})^+\) None \(3\) \(0\) \(6\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(2+\beta _{1})q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots\)
6498.2.a.bu 6498.a 1.a $3$ $51.887$ \(\Q(\zeta_{18})^+\) None \(3\) \(0\) \(6\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(2-\beta _{1})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)
6498.2.a.bv 6498.a 1.a $4$ $51.887$ \(\Q(\zeta_{20})^+\) None \(-4\) \(0\) \(-8\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-2+\beta _{1})q^{5}+(2+\beta _{2}+\cdots)q^{7}+\cdots\)
6498.2.a.bw 6498.a 1.a $4$ $51.887$ 4.4.40025.1 None \(-4\) \(0\) \(-2\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta _{1}q^{5}+(1+\beta _{2})q^{7}-q^{8}+\cdots\)
6498.2.a.bx 6498.a 1.a $4$ $51.887$ \(\Q(\zeta_{20})^+\) None \(-4\) \(0\) \(2\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)
6498.2.a.by 6498.a 1.a $4$ $51.887$ \(\Q(\zeta_{20})^+\) None \(4\) \(0\) \(-8\) \(6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-2+\beta _{1})q^{5}+(2+\beta _{2}+\cdots)q^{7}+\cdots\)
6498.2.a.bz 6498.a 1.a $4$ $51.887$ 4.4.40025.1 None \(4\) \(0\) \(-2\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-\beta _{1}q^{5}+(1+\beta _{2})q^{7}+q^{8}+\cdots\)
6498.2.a.ca 6498.a 1.a $4$ $51.887$ \(\Q(\zeta_{20})^+\) None \(4\) \(0\) \(2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)
6498.2.a.cb 6498.a 1.a $6$ $51.887$ 6.6.53327808.1 None \(-6\) \(0\) \(-6\) \(6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta _{5})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
6498.2.a.cc 6498.a 1.a $6$ $51.887$ 6.6.53327808.1 None \(-6\) \(0\) \(6\) \(6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta _{5})q^{5}+(1-\beta _{1})q^{7}+\cdots\)
6498.2.a.cd 6498.a 1.a $6$ $51.887$ 6.6.53327808.1 None \(6\) \(0\) \(-6\) \(6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta _{5})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
6498.2.a.ce 6498.a 1.a $6$ $51.887$ 6.6.53327808.1 None \(6\) \(0\) \(6\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta _{5})q^{5}+(1-\beta _{1})q^{7}+\cdots\)
6498.2.a.cf 6498.a 1.a $8$ $51.887$ 8.8.\(\cdots\).1 None \(-8\) \(0\) \(0\) \(-10\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{1}q^{5}+(-1-\beta _{6})q^{7}+\cdots\)
6498.2.a.cg 6498.a 1.a $8$ $51.887$ 8.8.\(\cdots\).1 None \(8\) \(0\) \(0\) \(-10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{1}q^{5}+(-1-\beta _{6})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6498))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6498)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(342))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2166))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3249))\)\(^{\oplus 2}\)