Properties

Label 1296.5
Level 1296
Weight 5
Dimension 82692
Nonzero newspaces 16
Sturm bound 466560
Trace bound 7

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Defining parameters

Level: \( N \) = \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(466560\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(1296))\).

Total New Old
Modular forms 188136 83196 104940
Cusp forms 185112 82692 102420
Eisenstein series 3024 504 2520

Trace form

\( 82692 q - 48 q^{2} - 54 q^{3} - 80 q^{4} - 60 q^{5} - 72 q^{6} - 60 q^{7} - 48 q^{8} - 18 q^{9} + O(q^{10}) \) \( 82692 q - 48 q^{2} - 54 q^{3} - 80 q^{4} - 60 q^{5} - 72 q^{6} - 60 q^{7} - 48 q^{8} - 18 q^{9} - 116 q^{10} - 36 q^{11} - 72 q^{12} - 100 q^{13} - 48 q^{14} - 54 q^{15} - 80 q^{16} - 105 q^{17} - 72 q^{18} - 87 q^{19} - 48 q^{20} - 90 q^{21} - 80 q^{22} - 36 q^{23} - 72 q^{24} + 605 q^{25} - 48 q^{26} - 54 q^{27} - 116 q^{28} - 3228 q^{29} - 72 q^{30} - 3372 q^{31} - 48 q^{32} - 162 q^{33} - 80 q^{34} - 39 q^{35} - 72 q^{36} + 3215 q^{37} - 48 q^{38} - 54 q^{39} - 80 q^{40} + 6612 q^{41} - 72 q^{42} + 3108 q^{43} - 48 q^{44} - 90 q^{45} - 244 q^{46} - 10836 q^{47} - 72 q^{48} - 2581 q^{49} - 48 q^{50} - 54 q^{51} - 80 q^{52} - 75 q^{53} - 72 q^{54} - 1337 q^{55} - 28860 q^{56} - 18 q^{57} - 33152 q^{58} - 5652 q^{59} - 72 q^{60} + 10460 q^{61} + 51036 q^{62} - 54 q^{63} + 39700 q^{64} + 54036 q^{65} - 72 q^{66} + 11268 q^{67} + 59388 q^{68} - 90 q^{69} + 19936 q^{70} - 51 q^{71} - 72 q^{72} - 13661 q^{73} - 70104 q^{74} - 54 q^{75} - 91520 q^{76} - 68028 q^{77} - 72 q^{78} - 18108 q^{79} - 128028 q^{80} - 162 q^{81} - 34280 q^{82} - 7956 q^{83} - 72 q^{84} + 12997 q^{85} + 95352 q^{86} - 54 q^{87} + 92128 q^{88} - 94617 q^{89} - 72 q^{90} - 80533 q^{91} - 48 q^{92} - 15210 q^{93} + 48 q^{94} + 150879 q^{95} - 72 q^{96} + 78780 q^{97} - 48 q^{98} + 173610 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(1296))\)

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
1296.5.b \(\chi_{1296}(487, \cdot)\) None 0 1
1296.5.e \(\chi_{1296}(161, \cdot)\) 1296.5.e.a 4 1
1296.5.e.b 4
1296.5.e.c 6
1296.5.e.d 8
1296.5.e.e 8
1296.5.e.f 8
1296.5.e.g 8
1296.5.e.h 12
1296.5.e.i 12
1296.5.e.j 24
1296.5.g \(\chi_{1296}(1135, \cdot)\) 1296.5.g.a 2 1
1296.5.g.b 2
1296.5.g.c 4
1296.5.g.d 4
1296.5.g.e 4
1296.5.g.f 8
1296.5.g.g 8
1296.5.g.h 8
1296.5.g.i 8
1296.5.g.j 16
1296.5.g.k 16
1296.5.g.l 16
1296.5.h \(\chi_{1296}(809, \cdot)\) None 0 1
1296.5.j \(\chi_{1296}(485, \cdot)\) n/a 760 2
1296.5.m \(\chi_{1296}(163, \cdot)\) n/a 760 2
1296.5.n \(\chi_{1296}(377, \cdot)\) None 0 2
1296.5.o \(\chi_{1296}(271, \cdot)\) n/a 192 2
1296.5.q \(\chi_{1296}(593, \cdot)\) n/a 190 2
1296.5.t \(\chi_{1296}(55, \cdot)\) None 0 2
1296.5.w \(\chi_{1296}(379, \cdot)\) n/a 1528 4
1296.5.x \(\chi_{1296}(53, \cdot)\) n/a 1528 4
1296.5.z \(\chi_{1296}(199, \cdot)\) None 0 6
1296.5.ba \(\chi_{1296}(127, \cdot)\) n/a 432 6
1296.5.bc \(\chi_{1296}(17, \cdot)\) n/a 426 6
1296.5.bf \(\chi_{1296}(89, \cdot)\) None 0 6
1296.5.bi \(\chi_{1296}(19, \cdot)\) n/a 3432 12
1296.5.bj \(\chi_{1296}(125, \cdot)\) n/a 3432 12
1296.5.bl \(\chi_{1296}(41, \cdot)\) None 0 18
1296.5.bm \(\chi_{1296}(31, \cdot)\) n/a 3888 18
1296.5.bo \(\chi_{1296}(65, \cdot)\) n/a 3870 18
1296.5.br \(\chi_{1296}(7, \cdot)\) None 0 18
1296.5.bt \(\chi_{1296}(43, \cdot)\) n/a 31032 36
1296.5.bu \(\chi_{1296}(5, \cdot)\) n/a 31032 36

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(1296))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(1296)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 15}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 15}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 2}\)