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Properties

Label 2310.2.a
Level $2310$
Weight $2$
Character orbit 2310.a
Rep. character $\chi_{2310}(1,\cdot)$
Character field $\Q$
Dimension $39$
Newform subspaces $30$
Sturm bound $1152$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2310.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 30 \)
Sturm bound: \(1152\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(13\), \(17\), \(19\), \(23\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2310))\).

Total New Old
Modular forms 592 39 553
Cusp forms 561 39 522
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.

\(2\)\(3\)\(5\)\(7\)\(11\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(+\)\(+\)\(-\)$-$\(1\)
\(+\)\(+\)\(+\)\(-\)\(+\)$-$\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)$+$\(1\)
\(+\)\(+\)\(-\)\(+\)\(+\)$-$\(2\)
\(+\)\(+\)\(-\)\(-\)\(+\)$+$\(1\)
\(+\)\(+\)\(-\)\(-\)\(-\)$-$\(2\)
\(+\)\(-\)\(+\)\(+\)\(+\)$-$\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)$+$\(1\)
\(+\)\(-\)\(+\)\(-\)\(+\)$+$\(2\)
\(+\)\(-\)\(+\)\(-\)\(-\)$-$\(1\)
\(+\)\(-\)\(-\)\(+\)\(+\)$+$\(2\)
\(+\)\(-\)\(-\)\(+\)\(-\)$-$\(2\)
\(+\)\(-\)\(-\)\(-\)\(+\)$-$\(1\)
\(-\)\(+\)\(+\)\(+\)\(+\)$-$\(1\)
\(-\)\(+\)\(+\)\(+\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)\(-\)\(-\)$-$\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)$+$\(1\)
\(-\)\(+\)\(-\)\(+\)\(-\)$-$\(2\)
\(-\)\(+\)\(-\)\(-\)\(+\)$-$\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)$+$\(1\)
\(-\)\(-\)\(+\)\(+\)\(-\)$-$\(2\)
\(-\)\(-\)\(+\)\(-\)\(+\)$-$\(2\)
\(-\)\(-\)\(-\)\(+\)\(+\)$-$\(1\)
\(-\)\(-\)\(-\)\(-\)\(-\)$-$\(3\)
Plus space\(+\)\(12\)
Minus space\(-\)\(27\)

Trace form

\( 39 q - q^{2} - q^{3} + 39 q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + 39 q^{9} + O(q^{10}) \) \( 39 q - q^{2} - q^{3} + 39 q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + 39 q^{9} - q^{10} - q^{11} - q^{12} - 14 q^{13} - q^{14} - q^{15} + 39 q^{16} + 14 q^{17} - q^{18} + 12 q^{19} - q^{20} - q^{21} + 7 q^{22} + 24 q^{23} - q^{24} + 39 q^{25} + 2 q^{26} - q^{27} - q^{28} + 2 q^{29} - q^{30} - 16 q^{31} - q^{32} - q^{33} - 18 q^{34} - q^{35} + 39 q^{36} + 10 q^{37} + 28 q^{38} - 14 q^{39} - q^{40} + 22 q^{41} + 7 q^{42} + 4 q^{43} - q^{44} - q^{45} + 24 q^{46} + 32 q^{47} - q^{48} + 39 q^{49} - q^{50} - 2 q^{51} - 14 q^{52} + 10 q^{53} - q^{54} - q^{55} - q^{56} - 20 q^{57} + 18 q^{58} + 36 q^{59} - q^{60} + 2 q^{61} + 32 q^{62} - q^{63} + 39 q^{64} + 18 q^{65} - q^{66} + 28 q^{67} + 14 q^{68} + 8 q^{69} + 7 q^{70} + 56 q^{71} - q^{72} + 22 q^{73} + 10 q^{74} - q^{75} + 12 q^{76} - q^{77} + 18 q^{78} + 32 q^{79} - q^{80} + 39 q^{81} - 10 q^{82} + 12 q^{83} - q^{84} - 18 q^{85} + 20 q^{86} + 34 q^{87} + 7 q^{88} - 10 q^{89} - q^{90} + 2 q^{91} + 24 q^{92} - 16 q^{93} + 48 q^{94} - 4 q^{95} - q^{96} + 14 q^{97} - q^{98} - q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2310))\) 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 7 11
2310.2.a.a 2310.a 1.a $1$ $18.445$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
2310.2.a.b 2310.a 1.a $1$ $18.445$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
2310.2.a.c 2310.a 1.a $1$ $18.445$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
2310.2.a.d 2310.a 1.a $1$ $18.445$ \(\Q\) None \(-1\) \(-1\) \(1\) \(1\) $+$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
2310.2.a.e 2310.a 1.a $1$ $18.445$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.f 2310.a 1.a $1$ $18.445$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.g 2310.a 1.a $1$ $18.445$ \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
2310.2.a.h 2310.a 1.a $1$ $18.445$ \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
2310.2.a.i 2310.a 1.a $1$ $18.445$ \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
2310.2.a.j 2310.a 1.a $1$ $18.445$ \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.k 2310.a 1.a $1$ $18.445$ \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.l 2310.a 1.a $1$ $18.445$ \(\Q\) None \(-1\) \(1\) \(1\) \(1\) $+$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
2310.2.a.m 2310.a 1.a $1$ $18.445$ \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) $-$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.n 2310.a 1.a $1$ $18.445$ \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.o 2310.a 1.a $1$ $18.445$ \(\Q\) None \(1\) \(-1\) \(1\) \(1\) $-$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
2310.2.a.p 2310.a 1.a $1$ $18.445$ \(\Q\) None \(1\) \(-1\) \(1\) \(1\) $-$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
2310.2.a.q 2310.a 1.a $1$ $18.445$ \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
2310.2.a.r 2310.a 1.a $1$ $18.445$ \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
2310.2.a.s 2310.a 1.a $1$ $18.445$ \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
2310.2.a.t 2310.a 1.a $1$ $18.445$ \(\Q\) None \(1\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
2310.2.a.u 2310.a 1.a $1$ $18.445$ \(\Q\) None \(1\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
2310.2.a.v 2310.a 1.a $1$ $18.445$ \(\Q\) None \(1\) \(1\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
2310.2.a.w 2310.a 1.a $2$ $18.445$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(-2\) \(2\) $+$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
2310.2.a.x 2310.a 1.a $2$ $18.445$ \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(2\) \(-2\) $+$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
2310.2.a.y 2310.a 1.a $2$ $18.445$ \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(2\) \(2\) $+$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
2310.2.a.z 2310.a 1.a $2$ $18.445$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(2\) \(-2\) $+$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.ba 2310.a 1.a $2$ $18.445$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(-2\) $-$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.bb 2310.a 1.a $2$ $18.445$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(2\) $-$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
2310.2.a.bc 2310.a 1.a $2$ $18.445$ \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(2\) \(-2\) $-$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.bd 2310.a 1.a $3$ $18.445$ 3.3.148.1 None \(3\) \(3\) \(3\) \(3\) $-$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2310))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2310)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\)\(^{\oplus 2}\)