Properties

Label 5070.2.a
Level $5070$
Weight $2$
Character orbit 5070.a
Rep. character $\chi_{5070}(1,\cdot)$
Character field $\Q$
Dimension $102$
Newform subspaces $53$
Sturm bound $2184$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5070.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 53 \)
Sturm bound: \(2184\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5070))\).

Total New Old
Modular forms 1148 102 1046
Cusp forms 1037 102 935
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.

\(2\)\(3\)\(5\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(7\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(40\)
Minus space\(-\)\(62\)

Trace form

\( 102 q - 2 q^{3} + 102 q^{4} - 4 q^{7} + 102 q^{9} + O(q^{10}) \) \( 102 q - 2 q^{3} + 102 q^{4} - 4 q^{7} + 102 q^{9} - 2 q^{10} - 12 q^{11} - 2 q^{12} - 12 q^{14} + 102 q^{16} - 8 q^{17} - 4 q^{21} - 12 q^{22} - 8 q^{23} + 102 q^{25} - 2 q^{27} - 4 q^{28} + 8 q^{29} - 2 q^{30} - 8 q^{31} + 12 q^{33} + 4 q^{34} + 4 q^{35} + 102 q^{36} + 16 q^{37} - 8 q^{38} - 2 q^{40} + 12 q^{41} + 4 q^{42} - 8 q^{43} - 12 q^{44} - 8 q^{46} + 16 q^{47} - 2 q^{48} + 102 q^{49} - 8 q^{51} + 16 q^{53} - 12 q^{55} - 12 q^{56} - 8 q^{57} + 4 q^{58} + 20 q^{59} - 4 q^{61} + 8 q^{62} - 4 q^{63} + 102 q^{64} + 4 q^{66} + 8 q^{67} - 8 q^{68} + 8 q^{69} + 4 q^{70} - 8 q^{71} + 20 q^{73} + 28 q^{74} - 2 q^{75} + 16 q^{77} - 8 q^{79} + 102 q^{81} + 16 q^{82} - 4 q^{84} + 12 q^{85} + 8 q^{87} - 12 q^{88} + 36 q^{89} - 2 q^{90} - 8 q^{92} - 16 q^{93} - 8 q^{95} + 28 q^{97} + 16 q^{98} - 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5070))\) 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 5 13
5070.2.a.a 5070.a 1.a $1$ $40.484$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5070.2.a.b 5070.a 1.a $1$ $40.484$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+3q^{7}+\cdots\)
5070.2.a.c 5070.a 1.a $1$ $40.484$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+3q^{7}+\cdots\)
5070.2.a.d 5070.a 1.a $1$ $40.484$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
5070.2.a.e 5070.a 1.a $1$ $40.484$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
5070.2.a.f 5070.a 1.a $1$ $40.484$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
5070.2.a.g 5070.a 1.a $1$ $40.484$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5070.2.a.h 5070.a 1.a $1$ $40.484$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5070.2.a.i 5070.a 1.a $1$ $40.484$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-5\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-5q^{7}+\cdots\)
5070.2.a.j 5070.a 1.a $1$ $40.484$ \(\Q\) None \(-1\) \(1\) \(-1\) \(2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5070.2.a.k 5070.a 1.a $1$ $40.484$ \(\Q\) None \(-1\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
5070.2.a.l 5070.a 1.a $1$ $40.484$ \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
5070.2.a.m 5070.a 1.a $1$ $40.484$ \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
5070.2.a.n 5070.a 1.a $1$ $40.484$ \(\Q\) None \(1\) \(-1\) \(-1\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5070.2.a.o 5070.a 1.a $1$ $40.484$ \(\Q\) None \(1\) \(-1\) \(-1\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5070.2.a.p 5070.a 1.a $1$ $40.484$ \(\Q\) None \(1\) \(-1\) \(-1\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5070.2.a.q 5070.a 1.a $1$ $40.484$ \(\Q\) None \(1\) \(-1\) \(1\) \(-3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-3q^{7}+\cdots\)
5070.2.a.r 5070.a 1.a $1$ $40.484$ \(\Q\) None \(1\) \(-1\) \(1\) \(-3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-3q^{7}+\cdots\)
5070.2.a.s 5070.a 1.a $1$ $40.484$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
5070.2.a.t 5070.a 1.a $1$ $40.484$ \(\Q\) None \(1\) \(1\) \(-1\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
5070.2.a.u 5070.a 1.a $1$ $40.484$ \(\Q\) None \(1\) \(1\) \(1\) \(-4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-4q^{7}+\cdots\)
5070.2.a.v 5070.a 1.a $1$ $40.484$ \(\Q\) None \(1\) \(1\) \(1\) \(-2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
5070.2.a.w 5070.a 1.a $1$ $40.484$ \(\Q\) None \(1\) \(1\) \(1\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
5070.2.a.x 5070.a 1.a $1$ $40.484$ \(\Q\) None \(1\) \(1\) \(1\) \(5\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+5q^{7}+\cdots\)
5070.2.a.y 5070.a 1.a $2$ $40.484$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(-2\) \(-4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
5070.2.a.z 5070.a 1.a $2$ $40.484$ \(\Q(\sqrt{13}) \) None \(-2\) \(-2\) \(-2\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5070.2.a.ba 5070.a 1.a $2$ $40.484$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(2\) \(-6\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots\)
5070.2.a.bb 5070.a 1.a $2$ $40.484$ \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(-2\) \(-3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
5070.2.a.bc 5070.a 1.a $2$ $40.484$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta q^{7}+\cdots\)
5070.2.a.bd 5070.a 1.a $2$ $40.484$ \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(2\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(1+\beta )q^{7}+\cdots\)
5070.2.a.be 5070.a 1.a $2$ $40.484$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(6\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots\)
5070.2.a.bf 5070.a 1.a $2$ $40.484$ \(\Q(\sqrt{13}) \) None \(2\) \(-2\) \(2\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(1+\beta )q^{7}+\cdots\)
5070.2.a.bg 5070.a 1.a $2$ $40.484$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(2\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
5070.2.a.bh 5070.a 1.a $2$ $40.484$ \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(-2\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5070.2.a.bi 5070.a 1.a $2$ $40.484$ \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(2\) \(3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta )q^{7}+\cdots\)
5070.2.a.bj 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(-3\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bk 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(-3\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bl 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(3\) \(8\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(3-\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bm 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(3\) \(8\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(3-\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bn 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(-3\) \(3\) \(-3\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
5070.2.a.bo 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(-3\) \(3\) \(-3\) \(10\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(3+\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bp 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(-3\) \(3\) \(3\) \(-6\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots\)
5070.2.a.bq 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(-3\) \(3\) \(3\) \(6\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.br 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(-3\) \(-8\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-3+\cdots)q^{7}+\cdots\)
5070.2.a.bs 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(-3\) \(-8\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-3+\cdots)q^{7}+\cdots\)
5070.2.a.bt 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(3\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bu 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(3\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bv 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(-3\) \(-6\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
5070.2.a.bw 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(-3\) \(6\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bx 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(3\) \(-10\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-3+\cdots)q^{7}+\cdots\)
5070.2.a.by 5070.a 1.a $3$ $40.484$ \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(3\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
5070.2.a.bz 5070.a 1.a $4$ $40.484$ 4.4.131472.2 None \(-4\) \(4\) \(4\) \(-2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-\beta _{1}q^{7}+\cdots\)
5070.2.a.ca 5070.a 1.a $4$ $40.484$ 4.4.131472.2 None \(4\) \(4\) \(-4\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5070))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5070)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(390))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(845))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2535))\)\(^{\oplus 2}\)