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Properties

Label 1340.2
Level 1340
Weight 2
Dimension 28396
Nonzero newspaces 24
Sturm bound 215424
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(215424\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1340))\).

Total New Old
Modular forms 55176 29172 26004
Cusp forms 52537 28396 24141
Eisenstein series 2639 776 1863

Trace form

\( 28396 q - 62 q^{2} + 4 q^{3} - 66 q^{4} - 188 q^{5} - 198 q^{6} - 4 q^{7} - 74 q^{8} - 134 q^{9} + O(q^{10}) \) \( 28396 q - 62 q^{2} + 4 q^{3} - 66 q^{4} - 188 q^{5} - 198 q^{6} - 4 q^{7} - 74 q^{8} - 134 q^{9} - 111 q^{10} - 66 q^{12} - 132 q^{13} - 66 q^{14} - 4 q^{15} - 182 q^{16} - 132 q^{17} - 54 q^{18} + 8 q^{19} - 91 q^{20} - 388 q^{21} - 66 q^{22} - 12 q^{23} - 66 q^{24} - 212 q^{25} - 206 q^{26} - 8 q^{27} - 66 q^{28} - 144 q^{29} - 99 q^{30} + 8 q^{31} - 82 q^{32} - 132 q^{33} - 66 q^{34} + 4 q^{35} - 222 q^{36} - 108 q^{37} - 66 q^{38} + 8 q^{39} - 91 q^{40} - 376 q^{41} - 66 q^{42} + 20 q^{43} - 66 q^{44} - 208 q^{45} - 198 q^{46} + 12 q^{47} - 66 q^{48} - 126 q^{49} - 71 q^{50} - 24 q^{51} - 58 q^{52} - 90 q^{53} - 66 q^{54} + 99 q^{55} - 198 q^{56} + 6 q^{57} - 82 q^{58} + 108 q^{59} - 99 q^{60} - 184 q^{61} - 66 q^{62} + 282 q^{63} - 66 q^{64} - 66 q^{65} - 264 q^{66} + 130 q^{67} - 108 q^{68} + 24 q^{69} - 99 q^{70} + 288 q^{71} - 42 q^{72} + 194 q^{73} - 66 q^{74} + 136 q^{75} - 198 q^{76} - 66 q^{78} + 138 q^{79} - 131 q^{80} - 140 q^{81} - 98 q^{82} + 54 q^{83} - 66 q^{84} - 174 q^{85} - 198 q^{86} + 24 q^{87} - 66 q^{88} - 120 q^{89} - 111 q^{90} - 8 q^{91} - 66 q^{92} - 148 q^{93} - 66 q^{94} - 8 q^{95} - 198 q^{96} - 188 q^{97} - 94 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1340))\)

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
1340.2.a \(\chi_{1340}(1, \cdot)\) 1340.2.a.a 1 1
1340.2.a.b 1
1340.2.a.c 1
1340.2.a.d 2
1340.2.a.e 2
1340.2.a.f 3
1340.2.a.g 3
1340.2.a.h 4
1340.2.a.i 5
1340.2.d \(\chi_{1340}(269, \cdot)\) 1340.2.d.a 2 1
1340.2.d.b 8
1340.2.d.c 24
1340.2.e \(\chi_{1340}(1339, \cdot)\) n/a 200 1
1340.2.h \(\chi_{1340}(1071, \cdot)\) n/a 136 1
1340.2.i \(\chi_{1340}(841, \cdot)\) 1340.2.i.a 2 2
1340.2.i.b 8
1340.2.i.c 16
1340.2.i.d 18
1340.2.j \(\chi_{1340}(133, \cdot)\) 1340.2.j.a 68 2
1340.2.k \(\chi_{1340}(403, \cdot)\) n/a 396 2
1340.2.n \(\chi_{1340}(239, \cdot)\) n/a 400 2
1340.2.o \(\chi_{1340}(29, \cdot)\) 1340.2.o.a 68 2
1340.2.r \(\chi_{1340}(231, \cdot)\) n/a 272 2
1340.2.u \(\chi_{1340}(81, \cdot)\) n/a 240 10
1340.2.x \(\chi_{1340}(163, \cdot)\) n/a 800 4
1340.2.y \(\chi_{1340}(97, \cdot)\) n/a 136 4
1340.2.z \(\chi_{1340}(271, \cdot)\) n/a 1360 10
1340.2.bc \(\chi_{1340}(119, \cdot)\) n/a 2000 10
1340.2.bd \(\chi_{1340}(9, \cdot)\) n/a 340 10
1340.2.bg \(\chi_{1340}(21, \cdot)\) n/a 440 20
1340.2.bj \(\chi_{1340}(107, \cdot)\) n/a 4000 20
1340.2.bk \(\chi_{1340}(53, \cdot)\) n/a 680 20
1340.2.bn \(\chi_{1340}(11, \cdot)\) n/a 2720 20
1340.2.bq \(\chi_{1340}(49, \cdot)\) n/a 680 20
1340.2.br \(\chi_{1340}(79, \cdot)\) n/a 4000 20
1340.2.bs \(\chi_{1340}(13, \cdot)\) n/a 1360 40
1340.2.bt \(\chi_{1340}(23, \cdot)\) n/a 8000 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1340))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1340)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(268))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(335))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(670))\)\(^{\oplus 2}\)