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Properties

Label 2358.2
Level 2358
Weight 2
Dimension 40751
Nonzero newspaces 16
Sturm bound 617760
Trace bound 2

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Defining parameters

Level: \( N \) = \( 2358 = 2 \cdot 3^{2} \cdot 131 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(617760\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2358))\).

Total New Old
Modular forms 156520 40751 115769
Cusp forms 152361 40751 111610
Eisenstein series 4159 0 4159

Trace form

\( 40751 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} + O(q^{10}) \) \( 40751 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} - 6 q^{11} + 4 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + 12 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} - 12 q^{23} + 6 q^{24} - 10 q^{25} - 8 q^{26} - 8 q^{28} + 12 q^{29} - 8 q^{31} + 2 q^{32} + 18 q^{33} - 6 q^{34} - 6 q^{36} + 16 q^{37} - 2 q^{38} + 18 q^{41} - 2 q^{43} + 12 q^{44} + 24 q^{46} - 12 q^{47} - 6 q^{48} - 6 q^{49} - 10 q^{50} - 18 q^{51} + 4 q^{52} - 48 q^{53} - 18 q^{54} + 4 q^{56} - 6 q^{57} + 12 q^{58} + 6 q^{59} + 16 q^{61} + 16 q^{62} + 24 q^{63} - 4 q^{64} + 10 q^{67} - 6 q^{68} + 48 q^{71} - 6 q^{72} - 44 q^{73} - 8 q^{74} + 30 q^{75} - 2 q^{76} - 12 q^{77} + 12 q^{78} - 8 q^{79} + 18 q^{81} - 36 q^{82} + 24 q^{83} + 12 q^{84} - 2 q^{86} - 36 q^{87} - 6 q^{88} - 24 q^{89} - 16 q^{91} - 12 q^{92} - 12 q^{94} + 10 q^{97} + 12 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2358))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2358.2.a \(\chi_{2358}(1, \cdot)\) 2358.2.a.a 1 1
2358.2.a.b 1
2358.2.a.c 1
2358.2.a.d 1
2358.2.a.e 1
2358.2.a.f 1
2358.2.a.g 1
2358.2.a.h 1
2358.2.a.i 1
2358.2.a.j 1
2358.2.a.k 1
2358.2.a.l 1
2358.2.a.m 1
2358.2.a.n 1
2358.2.a.o 1
2358.2.a.p 1
2358.2.a.q 1
2358.2.a.r 1
2358.2.a.s 1
2358.2.a.t 1
2358.2.a.u 1
2358.2.a.v 1
2358.2.a.w 1
2358.2.a.x 1
2358.2.a.y 1
2358.2.a.z 2
2358.2.a.ba 2
2358.2.a.bb 2
2358.2.a.bc 2
2358.2.a.bd 3
2358.2.a.be 3
2358.2.a.bf 4
2358.2.a.bg 6
2358.2.a.bh 6
2358.2.c \(\chi_{2358}(2357, \cdot)\) 2358.2.c.a 2 1
2358.2.c.b 2
2358.2.c.c 20
2358.2.c.d 20
2358.2.e \(\chi_{2358}(787, \cdot)\) n/a 260 2
2358.2.f \(\chi_{2358}(451, \cdot)\) n/a 220 4
2358.2.i \(\chi_{2358}(785, \cdot)\) n/a 264 2
2358.2.k \(\chi_{2358}(1511, \cdot)\) n/a 176 4
2358.2.m \(\chi_{2358}(307, \cdot)\) n/a 660 12
2358.2.n \(\chi_{2358}(61, \cdot)\) n/a 1056 8
2358.2.p \(\chi_{2358}(71, \cdot)\) n/a 528 12
2358.2.r \(\chi_{2358}(173, \cdot)\) n/a 1056 8
2358.2.u \(\chi_{2358}(193, \cdot)\) n/a 3168 24
2358.2.v \(\chi_{2358}(55, \cdot)\) n/a 2640 48
2358.2.w \(\chi_{2358}(47, \cdot)\) n/a 3168 24
2358.2.ba \(\chi_{2358}(17, \cdot)\) n/a 2112 48
2358.2.bc \(\chi_{2358}(7, \cdot)\) n/a 12672 96
2358.2.bf \(\chi_{2358}(23, \cdot)\) n/a 12672 96

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2358))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2358)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(131))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(262))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(393))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(786))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1179))\)\(^{\oplus 2}\)