Properties

Label 690.3
Level 690
Weight 3
Dimension 5784
Nonzero newspaces 12
Sturm bound 76032
Trace bound 4

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Defining parameters

Level: \( N \) = \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(76032\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(690))\).

Total New Old
Modular forms 26048 5784 20264
Cusp forms 24640 5784 18856
Eisenstein series 1408 0 1408

Trace form

\( 5784 q - 8 q^{2} - 8 q^{3} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 80 q^{9} + O(q^{10}) \) \( 5784 q - 8 q^{2} - 8 q^{3} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 80 q^{9} + 24 q^{10} + 32 q^{11} + 16 q^{12} + 56 q^{13} - 162 q^{15} - 32 q^{16} - 528 q^{17} - 440 q^{18} - 424 q^{19} - 104 q^{20} - 260 q^{21} - 64 q^{22} + 192 q^{23} + 192 q^{25} + 304 q^{26} + 604 q^{27} + 496 q^{28} + 616 q^{29} + 352 q^{30} + 1144 q^{31} + 32 q^{32} + 532 q^{33} + 320 q^{34} - 216 q^{35} + 48 q^{36} - 1016 q^{37} + 128 q^{38} - 448 q^{39} + 48 q^{40} - 416 q^{41} + 160 q^{42} - 560 q^{43} + 120 q^{45} - 80 q^{46} + 160 q^{47} - 32 q^{48} + 576 q^{49} - 184 q^{50} + 224 q^{51} - 208 q^{52} + 504 q^{53} + 136 q^{54} - 48 q^{55} - 128 q^{56} + 2108 q^{57} - 128 q^{58} + 1232 q^{59} + 320 q^{60} + 448 q^{61} + 160 q^{62} + 1708 q^{63} + 408 q^{65} + 992 q^{66} + 688 q^{67} + 176 q^{68} - 20 q^{69} + 96 q^{70} - 128 q^{71} - 272 q^{72} - 24 q^{73} - 942 q^{75} + 192 q^{76} + 256 q^{77} - 1592 q^{78} - 256 q^{79} - 3528 q^{81} - 448 q^{82} - 1088 q^{83} - 1184 q^{84} - 176 q^{85} - 192 q^{86} - 912 q^{87} + 128 q^{88} - 176 q^{89} - 72 q^{90} - 416 q^{91} + 32 q^{92} + 128 q^{93} + 640 q^{94} + 2732 q^{95} + 64 q^{96} + 4160 q^{97} + 3064 q^{98} + 2216 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(690))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
690.3.b \(\chi_{690}(599, \cdot)\) 690.3.b.a 88 1
690.3.c \(\chi_{690}(91, \cdot)\) 690.3.c.a 32 1
690.3.f \(\chi_{690}(229, \cdot)\) 690.3.f.a 48 1
690.3.g \(\chi_{690}(461, \cdot)\) 690.3.g.a 56 1
690.3.k \(\chi_{690}(277, \cdot)\) 690.3.k.a 40 2
690.3.k.b 48
690.3.l \(\chi_{690}(137, \cdot)\) n/a 192 2
690.3.o \(\chi_{690}(41, \cdot)\) n/a 640 10
690.3.p \(\chi_{690}(19, \cdot)\) n/a 480 10
690.3.s \(\chi_{690}(61, \cdot)\) n/a 320 10
690.3.t \(\chi_{690}(29, \cdot)\) n/a 960 10
690.3.u \(\chi_{690}(17, \cdot)\) n/a 1920 20
690.3.v \(\chi_{690}(13, \cdot)\) n/a 960 20

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(690))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(690)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 2}\)