↑

Properties

Label 6270.2.a
Level $6270$
Weight $2$
Character orbit 6270.a
Rep. character $\chi_{6270}(1,\cdot)$
Character field $\Q$
Dimension $119$
Newform subspaces $48$
Sturm bound $2880$
Trace bound $23$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 6270 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6270.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 48 \)
Sturm bound: \(2880\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(7\), \(13\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6270))\).

Total New Old
Modular forms 1456 119 1337
Cusp forms 1425 119 1306
Eisenstein series 31 0 31

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

\(2\)\(3\)\(5\)\(11\)\(19\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(+\)$+$\(2\)
\(+\)\(+\)\(+\)\(+\)\(-\)$-$\(6\)
\(+\)\(+\)\(+\)\(-\)\(+\)$-$\(6\)
\(+\)\(+\)\(+\)\(-\)\(-\)$+$\(1\)
\(+\)\(+\)\(-\)\(+\)\(+\)$-$\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)$+$\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)$+$\(3\)
\(+\)\(+\)\(-\)\(-\)\(-\)$-$\(5\)
\(+\)\(-\)\(+\)\(+\)\(+\)$-$\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)$+$\(4\)
\(+\)\(-\)\(+\)\(-\)\(+\)$+$\(3\)
\(+\)\(-\)\(+\)\(-\)\(-\)$-$\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)$+$\(4\)
\(+\)\(-\)\(-\)\(+\)\(-\)$-$\(4\)
\(+\)\(-\)\(-\)\(-\)\(+\)$-$\(5\)
\(+\)\(-\)\(-\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)\(+\)\(+\)$-$\(4\)
\(-\)\(+\)\(+\)\(+\)\(-\)$+$\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)$+$\(3\)
\(-\)\(+\)\(+\)\(-\)\(-\)$-$\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)$+$\(4\)
\(-\)\(+\)\(-\)\(+\)\(-\)$-$\(4\)
\(-\)\(+\)\(-\)\(-\)\(+\)$-$\(4\)
\(-\)\(+\)\(-\)\(-\)\(-\)$+$\(3\)
\(-\)\(-\)\(+\)\(+\)\(+\)$+$\(4\)
\(-\)\(-\)\(+\)\(+\)\(-\)$-$\(4\)
\(-\)\(-\)\(+\)\(-\)\(+\)$-$\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)$+$\(2\)
\(-\)\(-\)\(-\)\(+\)\(+\)$-$\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)$+$\(2\)
\(-\)\(-\)\(-\)\(-\)\(+\)$+$\(1\)
\(-\)\(-\)\(-\)\(-\)\(-\)$-$\(6\)
Plus space\(+\)\(44\)
Minus space\(-\)\(75\)

Trace form

\( 119 q - q^{2} - q^{3} + 119 q^{4} - q^{5} - q^{6} - 8 q^{7} - q^{8} + 119 q^{9} + O(q^{10}) \) \( 119 q - q^{2} - q^{3} + 119 q^{4} - q^{5} - q^{6} - 8 q^{7} - q^{8} + 119 q^{9} - q^{10} - q^{11} - q^{12} - 14 q^{13} - 8 q^{14} - q^{15} + 119 q^{16} - 18 q^{17} - q^{18} - q^{19} - q^{20} - 8 q^{21} - q^{22} - 24 q^{23} - q^{24} + 119 q^{25} - 14 q^{26} - q^{27} - 8 q^{28} + 2 q^{29} - q^{30} - q^{32} - q^{33} - 18 q^{34} + 24 q^{35} + 119 q^{36} - 38 q^{37} - q^{38} - 14 q^{39} - q^{40} + 22 q^{41} + 8 q^{42} + 20 q^{43} - q^{44} - q^{45} + 8 q^{46} + 16 q^{47} - q^{48} + 127 q^{49} - q^{50} + 14 q^{51} - 14 q^{52} + 10 q^{53} - q^{54} - q^{55} - 8 q^{56} - q^{57} + 18 q^{58} + 68 q^{59} - q^{60} + 2 q^{61} - 8 q^{63} + 119 q^{64} + 18 q^{65} - q^{66} + 60 q^{67} - 18 q^{68} + 8 q^{69} - 8 q^{70} + 24 q^{71} - q^{72} - 42 q^{73} - 6 q^{74} - q^{75} - q^{76} + 24 q^{77} + 18 q^{78} - 16 q^{79} - q^{80} + 119 q^{81} - 10 q^{82} + 44 q^{83} - 8 q^{84} + 14 q^{85} + 20 q^{86} + 2 q^{87} - q^{88} - 26 q^{89} - q^{90} - 16 q^{91} - 24 q^{92} - 16 q^{93} + 16 q^{94} - q^{95} - q^{96} - 2 q^{97} + 7 q^{98} - q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6270))\) 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 11 19
6270.2.a.a 6270.a 1.a $1$ $50.066$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
6270.2.a.b 6270.a 1.a $1$ $50.066$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) $+$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
6270.2.a.c 6270.a 1.a $1$ $50.066$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
6270.2.a.d 6270.a 1.a $1$ $50.066$ \(\Q\) None \(-1\) \(-1\) \(1\) \(2\) $+$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots\)
6270.2.a.e 6270.a 1.a $1$ $50.066$ \(\Q\) None \(-1\) \(-1\) \(1\) \(2\) $+$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots\)
6270.2.a.f 6270.a 1.a $1$ $50.066$ \(\Q\) None \(-1\) \(-1\) \(1\) \(4\) $+$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
6270.2.a.g 6270.a 1.a $1$ $50.066$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-2\) $+$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
6270.2.a.h 6270.a 1.a $1$ $50.066$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-2\) $+$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
6270.2.a.i 6270.a 1.a $1$ $50.066$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
6270.2.a.j 6270.a 1.a $1$ $50.066$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
6270.2.a.k 6270.a 1.a $1$ $50.066$ \(\Q\) None \(-1\) \(1\) \(-1\) \(2\) $+$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
6270.2.a.l 6270.a 1.a $1$ $50.066$ \(\Q\) None \(-1\) \(1\) \(1\) \(-4\) $+$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
6270.2.a.m 6270.a 1.a $1$ $50.066$ \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
6270.2.a.n 6270.a 1.a $1$ $50.066$ \(\Q\) None \(1\) \(-1\) \(1\) \(-2\) $-$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
6270.2.a.o 6270.a 1.a $1$ $50.066$ \(\Q\) None \(1\) \(1\) \(-1\) \(-2\) $-$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
6270.2.a.p 6270.a 1.a $1$ $50.066$ \(\Q\) None \(1\) \(1\) \(-1\) \(-2\) $-$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
6270.2.a.q 6270.a 1.a $1$ $50.066$ \(\Q\) None \(1\) \(1\) \(-1\) \(2\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
6270.2.a.r 6270.a 1.a $1$ $50.066$ \(\Q\) None \(1\) \(1\) \(1\) \(-2\) $-$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
6270.2.a.s 6270.a 1.a $2$ $50.066$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(-2\) \(-2\) $+$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
6270.2.a.t 6270.a 1.a $2$ $50.066$ \(\Q(\sqrt{10}) \) None \(-2\) \(-2\) \(2\) \(-4\) $+$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
6270.2.a.u 6270.a 1.a $2$ $50.066$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) $+$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta q^{7}+\cdots\)
6270.2.a.v 6270.a 1.a $2$ $50.066$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(4\) $+$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(2+\beta )q^{7}+\cdots\)
6270.2.a.w 6270.a 1.a $2$ $50.066$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(2\) \(0\) $+$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta q^{7}+\cdots\)
6270.2.a.x 6270.a 1.a $2$ $50.066$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(-2\) $-$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
6270.2.a.y 6270.a 1.a $2$ $50.066$ \(\Q(\sqrt{7}) \) None \(2\) \(-2\) \(2\) \(-2\) $-$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
6270.2.a.z 6270.a 1.a $2$ $50.066$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(2\) \(-6\) $-$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-3+\cdots)q^{7}+\cdots\)
6270.2.a.ba 6270.a 1.a $3$ $50.066$ 3.3.3028.1 None \(-3\) \(-3\) \(-3\) \(-6\) $+$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
6270.2.a.bb 6270.a 1.a $3$ $50.066$ 3.3.229.1 None \(-3\) \(-3\) \(-3\) \(4\) $+$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(1+\beta _{2})q^{7}+\cdots\)
6270.2.a.bc 6270.a 1.a $3$ $50.066$ 3.3.1492.1 None \(-3\) \(-3\) \(3\) \(-2\) $+$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
6270.2.a.bd 6270.a 1.a $3$ $50.066$ 3.3.404.1 None \(-3\) \(3\) \(-3\) \(-4\) $+$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
6270.2.a.be 6270.a 1.a $3$ $50.066$ 3.3.2292.1 None \(-3\) \(3\) \(-3\) \(-2\) $+$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
6270.2.a.bf 6270.a 1.a $3$ $50.066$ 3.3.756.1 None \(-3\) \(3\) \(3\) \(6\) $+$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
6270.2.a.bg 6270.a 1.a $3$ $50.066$ 3.3.316.1 None \(3\) \(-3\) \(-3\) \(-2\) $-$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
6270.2.a.bh 6270.a 1.a $3$ $50.066$ 3.3.564.1 None \(3\) \(3\) \(-3\) \(0\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
6270.2.a.bi 6270.a 1.a $3$ $50.066$ 3.3.148.1 None \(3\) \(3\) \(3\) \(-2\) $-$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
6270.2.a.bj 6270.a 1.a $3$ $50.066$ 3.3.837.1 None \(3\) \(3\) \(3\) \(6\) $-$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots\)
6270.2.a.bk 6270.a 1.a $4$ $50.066$ 4.4.8468.1 None \(-4\) \(4\) \(4\) \(-2\) $+$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
6270.2.a.bl 6270.a 1.a $4$ $50.066$ 4.4.88404.1 None \(4\) \(-4\) \(-4\) \(-2\) $-$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+\beta _{2}q^{7}+\cdots\)
6270.2.a.bm 6270.a 1.a $4$ $50.066$ 4.4.11348.1 None \(4\) \(-4\) \(4\) \(-4\) $-$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
6270.2.a.bn 6270.a 1.a $4$ $50.066$ 4.4.29268.1 None \(4\) \(-4\) \(4\) \(4\) $-$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
6270.2.a.bo 6270.a 1.a $4$ $50.066$ 4.4.20308.1 None \(4\) \(-4\) \(4\) \(4\) $-$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
6270.2.a.bp 6270.a 1.a $4$ $50.066$ 4.4.7232.1 None \(4\) \(4\) \(-4\) \(-4\) $-$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
6270.2.a.bq 6270.a 1.a $5$ $50.066$ 5.5.1096132.1 None \(-5\) \(-5\) \(5\) \(8\) $+$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(2+\beta _{4})q^{7}+\cdots\)
6270.2.a.br 6270.a 1.a $5$ $50.066$ 5.5.2508628.1 None \(-5\) \(5\) \(5\) \(0\) $+$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-\beta _{3}q^{7}+\cdots\)
6270.2.a.bs 6270.a 1.a $5$ $50.066$ 5.5.10674100.1 None \(5\) \(-5\) \(-5\) \(2\) $-$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
6270.2.a.bt 6270.a 1.a $5$ $50.066$ 5.5.2873476.1 None \(5\) \(5\) \(-5\) \(2\) $-$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-\beta _{2}q^{7}+\cdots\)
6270.2.a.bu 6270.a 1.a $5$ $50.066$ 5.5.220036.1 None \(5\) \(5\) \(5\) \(4\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
6270.2.a.bv 6270.a 1.a $6$ $50.066$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-6\) \(-6\) \(-6\) \(0\) $+$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6270))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6270)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(418))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(570))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(627))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1045))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1254))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2090))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3135))\)\(^{\oplus 2}\)