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Properties

Label 2916.3
Level 2916
Weight 3
Dimension 217080
Nonzero newspaces 12
Sturm bound 1417176
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2916 = 2^{2} \cdot 3^{6} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(1417176\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(2916))\).

Total New Old
Modular forms 475632 218376 257256
Cusp forms 469152 217080 252072
Eisenstein series 6480 1296 5184

Trace form

\( 217080 q - 108 q^{2} - 180 q^{4} - 216 q^{5} - 162 q^{6} - 108 q^{8} - 324 q^{9} + O(q^{10}) \) \( 217080 q - 108 q^{2} - 180 q^{4} - 216 q^{5} - 162 q^{6} - 108 q^{8} - 324 q^{9} - 252 q^{10} - 162 q^{12} - 360 q^{13} - 108 q^{14} - 180 q^{16} - 216 q^{17} - 162 q^{18} - 108 q^{20} - 324 q^{21} - 180 q^{22} - 162 q^{24} - 360 q^{25} - 108 q^{26} - 324 q^{28} - 216 q^{29} - 162 q^{30} - 108 q^{32} - 324 q^{33} - 180 q^{34} - 162 q^{36} - 504 q^{37} - 108 q^{38} - 180 q^{40} - 216 q^{41} - 162 q^{42} - 108 q^{44} - 324 q^{45} - 252 q^{46} - 162 q^{48} - 360 q^{49} - 108 q^{50} - 180 q^{52} - 216 q^{53} - 162 q^{54} - 108 q^{56} - 324 q^{57} - 180 q^{58} - 162 q^{60} - 360 q^{61} - 108 q^{62} - 252 q^{64} + 594 q^{65} - 162 q^{66} + 702 q^{67} - 108 q^{68} - 324 q^{69} - 180 q^{70} + 972 q^{71} - 162 q^{72} + 63 q^{73} - 108 q^{74} - 180 q^{76} + 432 q^{77} - 162 q^{78} + 108 q^{79} - 135 q^{80} - 324 q^{81} - 405 q^{82} - 324 q^{83} - 162 q^{84} - 900 q^{85} - 108 q^{86} - 180 q^{88} - 1431 q^{89} - 162 q^{90} - 891 q^{91} - 108 q^{92} - 324 q^{93} - 180 q^{94} - 1620 q^{95} - 162 q^{96} - 1278 q^{97} - 108 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(2916))\)

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
2916.3.c \(\chi_{2916}(1457, \cdot)\) 2916.3.c.a 36 1
2916.3.c.b 36
2916.3.d \(\chi_{2916}(1459, \cdot)\) n/a 420 1
2916.3.f \(\chi_{2916}(487, \cdot)\) n/a 840 2
2916.3.g \(\chi_{2916}(485, \cdot)\) n/a 144 2
2916.3.j \(\chi_{2916}(163, \cdot)\) n/a 2556 6
2916.3.k \(\chi_{2916}(161, \cdot)\) n/a 432 6
2916.3.n \(\chi_{2916}(55, \cdot)\) n/a 7632 18
2916.3.o \(\chi_{2916}(53, \cdot)\) n/a 1296 18
2916.3.r \(\chi_{2916}(19, \cdot)\) n/a 17388 54
2916.3.s \(\chi_{2916}(17, \cdot)\) n/a 2916 54
2916.3.v \(\chi_{2916}(7, \cdot)\) n/a 157140 162
2916.3.w \(\chi_{2916}(5, \cdot)\) n/a 26244 162

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(2916))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(2916)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(486))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(729))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(972))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1458))\)\(^{\oplus 2}\)