Properties

Label 2310.2.a
Level 2310
Weight 2
Character orbit a
Rep. character \(\chi_{2310}(1,\cdot)\)
Character field \(\Q\)
Dimension 39
Newforms 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: \(\Q\)
Newforms: \( 30 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2310))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 7 11
2310.2.a.a \(1\) \(18.445\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
2310.2.a.b \(1\) \(18.445\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
2310.2.a.c \(1\) \(18.445\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
2310.2.a.d \(1\) \(18.445\) \(\Q\) None \(-1\) \(-1\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
2310.2.a.e \(1\) \(18.445\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.f \(1\) \(18.445\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.g \(1\) \(18.445\) \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
2310.2.a.h \(1\) \(18.445\) \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
2310.2.a.i \(1\) \(18.445\) \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
2310.2.a.j \(1\) \(18.445\) \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.k \(1\) \(18.445\) \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.l \(1\) \(18.445\) \(\Q\) None \(-1\) \(1\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
2310.2.a.m \(1\) \(18.445\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.n \(1\) \(18.445\) \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.o \(1\) \(18.445\) \(\Q\) None \(1\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
2310.2.a.p \(1\) \(18.445\) \(\Q\) None \(1\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
2310.2.a.q \(1\) \(18.445\) \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
2310.2.a.r \(1\) \(18.445\) \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
2310.2.a.s \(1\) \(18.445\) \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
2310.2.a.t \(1\) \(18.445\) \(\Q\) None \(1\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
2310.2.a.u \(1\) \(18.445\) \(\Q\) None \(1\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
2310.2.a.v \(1\) \(18.445\) \(\Q\) None \(1\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
2310.2.a.w \(2\) \(18.445\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(-2\) \(2\) \(+\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
2310.2.a.x \(2\) \(18.445\) \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(2\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
2310.2.a.y \(2\) \(18.445\) \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(2\) \(2\) \(+\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
2310.2.a.z \(2\) \(18.445\) \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(2\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.ba \(2\) \(18.445\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.bb \(2\) \(18.445\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(2\) \(-\) \(+\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
2310.2.a.bc \(2\) \(18.445\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(2\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2310.2.a.bd \(3\) \(18.445\) 3.3.148.1 None \(3\) \(3\) \(3\) \(3\) \(-\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)

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

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