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Properties

Label 324.5
Level 324
Weight 5
Dimension 5320
Nonzero newspaces 8
Sturm bound 29160
Trace bound 1

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Defining parameters

Level: \( N \) = \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(29160\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(324))\).

Total New Old
Modular forms 11934 5432 6502
Cusp forms 11394 5320 6074
Eisenstein series 540 112 428

Trace form

\( 5320 q - 12 q^{2} - 20 q^{4} - 33 q^{5} - 18 q^{6} - 39 q^{7} - 15 q^{8} - 36 q^{9} + O(q^{10}) \) \( 5320 q - 12 q^{2} - 20 q^{4} - 33 q^{5} - 18 q^{6} - 39 q^{7} - 15 q^{8} - 36 q^{9} - 61 q^{10} - 18 q^{11} - 18 q^{12} + 215 q^{13} + 843 q^{14} + 352 q^{16} - 30 q^{17} - 18 q^{18} - 1332 q^{19} - 1965 q^{20} + 2259 q^{21} - 1128 q^{22} + 4275 q^{23} - 18 q^{24} + 411 q^{25} + 4701 q^{26} - 1431 q^{27} - 105 q^{28} - 4263 q^{29} - 18 q^{30} - 2781 q^{31} - 4962 q^{32} - 3249 q^{33} - 1114 q^{34} + 5346 q^{35} - 18 q^{36} + 2576 q^{37} + 6066 q^{38} + 9305 q^{40} + 10560 q^{41} + 18297 q^{42} + 864 q^{43} - 6063 q^{44} - 11268 q^{45} - 25497 q^{46} - 23895 q^{47} - 35163 q^{48} - 1865 q^{49} - 55122 q^{50} - 12348 q^{51} - 7021 q^{52} + 6 q^{53} + 13464 q^{54} + 9414 q^{55} + 72081 q^{56} + 21132 q^{57} + 36881 q^{58} + 41940 q^{59} + 58131 q^{60} + 17039 q^{61} + 51069 q^{62} + 14040 q^{63} - 4439 q^{64} + 19911 q^{65} - 34650 q^{66} - 22878 q^{67} - 115764 q^{68} - 47484 q^{69} - 23193 q^{70} - 19764 q^{71} - 18 q^{72} - 7651 q^{73} - 6801 q^{74} - 56250 q^{75} + 17070 q^{76} - 39993 q^{77} - 747 q^{78} + 10353 q^{79} + 63966 q^{80} + 11556 q^{81} + 37406 q^{82} + 53973 q^{83} - 747 q^{84} - 12992 q^{85} + 2544 q^{86} + 126000 q^{87} - 45444 q^{88} + 149631 q^{89} - 116757 q^{90} + 10713 q^{91} - 122187 q^{92} + 33516 q^{93} - 13767 q^{94} - 115632 q^{95} + 91359 q^{96} - 36862 q^{97} + 235965 q^{98} - 169380 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(324))\)

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
324.5.c \(\chi_{324}(161, \cdot)\) 324.5.c.a 8 1
324.5.c.b 8
324.5.d \(\chi_{324}(163, \cdot)\) 324.5.d.a 2 1
324.5.d.b 2
324.5.d.c 10
324.5.d.d 10
324.5.d.e 22
324.5.d.f 22
324.5.d.g 24
324.5.f \(\chi_{324}(55, \cdot)\) n/a 188 2
324.5.g \(\chi_{324}(53, \cdot)\) 324.5.g.a 2 2
324.5.g.b 2
324.5.g.c 4
324.5.g.d 4
324.5.g.e 4
324.5.g.f 16
324.5.j \(\chi_{324}(19, \cdot)\) n/a 420 6
324.5.k \(\chi_{324}(17, \cdot)\) 324.5.k.a 72 6
324.5.n \(\chi_{324}(7, \cdot)\) n/a 3852 18
324.5.o \(\chi_{324}(5, \cdot)\) n/a 648 18

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(324))\) into lower level spaces

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