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Properties

Label 324.6
Level 324
Weight 6
Dimension 6664
Nonzero newspaces 8
Sturm bound 34992
Trace bound 1

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Defining parameters

Level: \( N \) = \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(34992\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(324))\).

Total New Old
Modular forms 14850 6776 8074
Cusp forms 14310 6664 7646
Eisenstein series 540 112 428

Trace form

\( 6664 q - 12 q^{2} - 20 q^{4} + 63 q^{5} - 18 q^{6} - 87 q^{7} - 9 q^{8} - 36 q^{9} + O(q^{10}) \) \( 6664 q - 12 q^{2} - 20 q^{4} + 63 q^{5} - 18 q^{6} - 87 q^{7} - 9 q^{8} - 36 q^{9} + 35 q^{10} + 1257 q^{11} - 18 q^{12} - 691 q^{13} - 1527 q^{14} + 2488 q^{16} + 3450 q^{17} - 18 q^{18} + 522 q^{19} - 1251 q^{20} - 13779 q^{21} - 6576 q^{22} - 8403 q^{23} - 18 q^{24} + 17307 q^{25} - 27 q^{26} + 17523 q^{27} + 13191 q^{28} - 11679 q^{29} - 18 q^{30} - 17145 q^{31} - 7242 q^{32} - 36783 q^{33} - 19234 q^{34} - 11184 q^{35} - 18 q^{36} + 57842 q^{37} - 14886 q^{38} - 7945 q^{40} - 196917 q^{41} - 52173 q^{42} - 12447 q^{43} + 316071 q^{44} + 135990 q^{45} + 160839 q^{46} + 141921 q^{47} + 66411 q^{48} + 10195 q^{49} - 249432 q^{50} - 126315 q^{51} - 162655 q^{52} - 147594 q^{53} - 347148 q^{54} - 125730 q^{55} - 408483 q^{56} - 41562 q^{57} - 7441 q^{58} + 95097 q^{59} + 329805 q^{60} + 159173 q^{61} + 922869 q^{62} + 266274 q^{63} + 376009 q^{64} - 18297 q^{65} + 39222 q^{66} - 93789 q^{67} - 810006 q^{68} + 94914 q^{69} - 280071 q^{70} + 339060 q^{71} - 18 q^{72} + 149285 q^{73} - 20415 q^{74} - 56250 q^{75} - 107934 q^{76} - 563895 q^{77} + 2169 q^{78} + 54141 q^{79} - 455004 q^{81} + 45782 q^{82} - 263763 q^{83} - 2205 q^{84} + 193120 q^{85} + 279228 q^{86} + 405936 q^{87} + 319044 q^{88} - 445659 q^{89} + 856215 q^{90} + 141297 q^{91} - 106185 q^{92} + 1675710 q^{93} - 559731 q^{94} + 1074756 q^{95} - 1285965 q^{96} + 490337 q^{97} - 2615967 q^{98} - 908586 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(324))\)

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
324.6.a \(\chi_{324}(1, \cdot)\) 324.6.a.a 3 1
324.6.a.b 3
324.6.a.c 4
324.6.a.d 5
324.6.a.e 5
324.6.b \(\chi_{324}(323, \cdot)\) n/a 116 1
324.6.e \(\chi_{324}(109, \cdot)\) 324.6.e.a 2 2
324.6.e.b 2
324.6.e.c 2
324.6.e.d 2
324.6.e.e 4
324.6.e.f 4
324.6.e.g 4
324.6.e.h 6
324.6.e.i 6
324.6.e.j 8
324.6.h \(\chi_{324}(107, \cdot)\) n/a 236 2
324.6.i \(\chi_{324}(37, \cdot)\) 324.6.i.a 90 6
324.6.l \(\chi_{324}(35, \cdot)\) n/a 528 6
324.6.m \(\chi_{324}(13, \cdot)\) n/a 810 18
324.6.p \(\chi_{324}(11, \cdot)\) n/a 4824 18

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(324))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(324)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 2}\)