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Properties

Label 1340.3
Level 1340
Weight 3
Dimension 57180
Nonzero newspaces 24
Sturm bound 323136
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(323136\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1340))\).

Total New Old
Modular forms 109032 57964 51068
Cusp forms 106392 57180 49212
Eisenstein series 2640 784 1856

Trace form

\( 57180 q - 62 q^{2} - 4 q^{3} - 58 q^{4} - 178 q^{5} - 166 q^{6} + 28 q^{7} - 50 q^{8} - 116 q^{9} + O(q^{10}) \) \( 57180 q - 62 q^{2} - 4 q^{3} - 58 q^{4} - 178 q^{5} - 166 q^{6} + 28 q^{7} - 50 q^{8} - 116 q^{9} - 111 q^{10} - 40 q^{11} - 146 q^{12} - 136 q^{13} - 178 q^{14} - 4 q^{15} - 294 q^{16} - 88 q^{17} - 110 q^{18} - 11 q^{20} - 356 q^{21} + 94 q^{22} + 92 q^{23} + 222 q^{24} - 282 q^{25} + 18 q^{26} - 64 q^{27} + 14 q^{28} - 196 q^{29} - 179 q^{30} + 56 q^{31} - 322 q^{32} - 332 q^{33} - 378 q^{34} - 196 q^{35} - 382 q^{36} - 296 q^{37} - 226 q^{38} - 51 q^{40} - 292 q^{41} + 174 q^{42} + 60 q^{43} + 94 q^{44} + 242 q^{45} + 74 q^{46} + 156 q^{47} - 66 q^{48} + 204 q^{49} - 271 q^{50} - 8 q^{51} - 178 q^{52} - 610 q^{53} - 290 q^{54} - 969 q^{55} - 486 q^{56} - 1486 q^{57} + 6 q^{58} - 924 q^{59} - 179 q^{60} - 1996 q^{61} + 94 q^{62} - 1054 q^{63} + 62 q^{64} - 830 q^{65} - 292 q^{66} + 146 q^{67} + 140 q^{68} - 680 q^{69} + 61 q^{70} + 928 q^{71} + 78 q^{72} + 1146 q^{73} + 342 q^{74} + 1312 q^{75} - 198 q^{76} + 1120 q^{77} + 94 q^{78} + 2002 q^{79} + 189 q^{80} + 3306 q^{81} - 298 q^{82} + 1374 q^{83} - 130 q^{84} + 406 q^{85} - 646 q^{86} + 32 q^{87} - 386 q^{88} + 924 q^{89} + 129 q^{90} + 504 q^{91} + 174 q^{92} + 724 q^{93} + 142 q^{94} - 128 q^{95} + 314 q^{96} + 264 q^{97} - 270 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1340))\)

We only show spaces with odd 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
1340.3.b \(\chi_{1340}(401, \cdot)\) 1340.3.b.a 2 1
1340.3.b.b 42
1340.3.c \(\chi_{1340}(671, \cdot)\) n/a 264 1
1340.3.f \(\chi_{1340}(939, \cdot)\) n/a 396 1
1340.3.g \(\chi_{1340}(669, \cdot)\) 1340.3.g.a 68 1
1340.3.l \(\chi_{1340}(537, \cdot)\) n/a 132 2
1340.3.m \(\chi_{1340}(267, \cdot)\) n/a 808 2
1340.3.p \(\chi_{1340}(171, \cdot)\) n/a 544 2
1340.3.q \(\chi_{1340}(641, \cdot)\) 1340.3.q.a 92 2
1340.3.s \(\chi_{1340}(909, \cdot)\) n/a 136 2
1340.3.t \(\chi_{1340}(439, \cdot)\) n/a 808 2
1340.3.v \(\chi_{1340}(507, \cdot)\) n/a 1616 4
1340.3.w \(\chi_{1340}(37, \cdot)\) n/a 272 4
1340.3.ba \(\chi_{1340}(109, \cdot)\) n/a 680 10
1340.3.bb \(\chi_{1340}(59, \cdot)\) n/a 4040 10
1340.3.be \(\chi_{1340}(91, \cdot)\) n/a 2720 10
1340.3.bf \(\chi_{1340}(161, \cdot)\) n/a 440 10
1340.3.bh \(\chi_{1340}(3, \cdot)\) n/a 8080 20
1340.3.bi \(\chi_{1340}(193, \cdot)\) n/a 1360 20
1340.3.bl \(\chi_{1340}(19, \cdot)\) n/a 8080 20
1340.3.bm \(\chi_{1340}(69, \cdot)\) n/a 1360 20
1340.3.bo \(\chi_{1340}(41, \cdot)\) n/a 920 20
1340.3.bp \(\chi_{1340}(71, \cdot)\) n/a 5440 20
1340.3.bu \(\chi_{1340}(17, \cdot)\) n/a 2720 40
1340.3.bv \(\chi_{1340}(7, \cdot)\) n/a 16160 40

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1340))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1340)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(268))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(335))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(670))\)\(^{\oplus 2}\)