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Properties

Label 1296.2
Level 1296
Weight 2
Dimension 20484
Nonzero newspaces 16
Sturm bound 186624
Trace bound 7

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Defining parameters

Level: \( N \) = \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(186624\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1296))\).

Total New Old
Modular forms 48168 20988 27180
Cusp forms 45145 20484 24661
Eisenstein series 3023 504 2519

Trace form

\( 20484q - 48q^{2} - 54q^{3} - 80q^{4} - 60q^{5} - 72q^{6} - 60q^{7} - 48q^{8} - 18q^{9} + O(q^{10}) \) \( 20484q - 48q^{2} - 54q^{3} - 80q^{4} - 60q^{5} - 72q^{6} - 60q^{7} - 48q^{8} - 18q^{9} - 116q^{10} - 36q^{11} - 72q^{12} - 100q^{13} - 48q^{14} - 54q^{15} - 80q^{16} - 111q^{17} - 72q^{18} - 87q^{19} - 48q^{20} - 90q^{21} - 80q^{22} - 36q^{23} - 72q^{24} - 25q^{25} - 48q^{26} - 54q^{27} - 116q^{28} - 84q^{29} - 72q^{30} - 78q^{31} - 48q^{32} - 162q^{33} - 80q^{34} - 69q^{35} - 72q^{36} - 169q^{37} - 48q^{38} - 54q^{39} - 80q^{40} - 36q^{41} - 72q^{42} - 78q^{43} - 48q^{44} - 90q^{45} - 100q^{46} - 54q^{47} - 72q^{48} - 187q^{49} - 48q^{50} - 54q^{51} - 80q^{52} - 45q^{53} - 72q^{54} - 77q^{55} + 36q^{56} - 18q^{57} - 32q^{58} - 18q^{59} - 72q^{60} - 52q^{61} + 84q^{62} - 54q^{63} - 44q^{64} - 12q^{65} - 72q^{66} - 36q^{67} + 108q^{68} - 90q^{69} + 64q^{70} + 21q^{71} - 72q^{72} + 19q^{73} + 120q^{74} - 54q^{75} + 64q^{76} + 36q^{77} - 72q^{78} - 36q^{79} + 132q^{80} - 162q^{81} - 152q^{82} - 6q^{83} - 72q^{84} - 17q^{85} + 72q^{86} - 54q^{87} - 32q^{88} + 69q^{89} - 72q^{90} - q^{91} - 48q^{92} + 18q^{93} - 96q^{94} + 249q^{95} - 72q^{96} - 96q^{97} - 48q^{98} + 108q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1296))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1296.2.a \(\chi_{1296}(1, \cdot)\) 1296.2.a.a 1 1
1296.2.a.b 1
1296.2.a.c 1
1296.2.a.d 1
1296.2.a.e 1
1296.2.a.f 1
1296.2.a.g 1
1296.2.a.h 1
1296.2.a.i 1
1296.2.a.j 1
1296.2.a.k 1
1296.2.a.l 1
1296.2.a.m 2
1296.2.a.n 2
1296.2.a.o 2
1296.2.a.p 2
1296.2.a.q 2
1296.2.c \(\chi_{1296}(1295, \cdot)\) 1296.2.c.a 2 1
1296.2.c.b 2
1296.2.c.c 2
1296.2.c.d 2
1296.2.c.e 4
1296.2.c.f 4
1296.2.c.g 8
1296.2.d \(\chi_{1296}(649, \cdot)\) None 0 1
1296.2.f \(\chi_{1296}(647, \cdot)\) None 0 1
1296.2.i \(\chi_{1296}(433, \cdot)\) 1296.2.i.a 2 2
1296.2.i.b 2
1296.2.i.c 2
1296.2.i.d 2
1296.2.i.e 2
1296.2.i.f 2
1296.2.i.g 2
1296.2.i.h 2
1296.2.i.i 2
1296.2.i.j 2
1296.2.i.k 2
1296.2.i.l 2
1296.2.i.m 2
1296.2.i.n 2
1296.2.i.o 2
1296.2.i.p 2
1296.2.i.q 2
1296.2.i.r 4
1296.2.i.s 4
1296.2.i.t 4
1296.2.k \(\chi_{1296}(325, \cdot)\) n/a 184 2
1296.2.l \(\chi_{1296}(323, \cdot)\) n/a 184 2
1296.2.p \(\chi_{1296}(215, \cdot)\) None 0 2
1296.2.r \(\chi_{1296}(217, \cdot)\) None 0 2
1296.2.s \(\chi_{1296}(431, \cdot)\) 1296.2.s.a 2 2
1296.2.s.b 2
1296.2.s.c 2
1296.2.s.d 2
1296.2.s.e 2
1296.2.s.f 2
1296.2.s.g 4
1296.2.s.h 4
1296.2.s.i 4
1296.2.s.j 8
1296.2.s.k 8
1296.2.s.l 8
1296.2.u \(\chi_{1296}(145, \cdot)\) n/a 102 6
1296.2.v \(\chi_{1296}(107, \cdot)\) n/a 376 4
1296.2.y \(\chi_{1296}(109, \cdot)\) n/a 376 4
1296.2.bb \(\chi_{1296}(73, \cdot)\) None 0 6
1296.2.bd \(\chi_{1296}(71, \cdot)\) None 0 6
1296.2.be \(\chi_{1296}(143, \cdot)\) n/a 108 6
1296.2.bg \(\chi_{1296}(49, \cdot)\) n/a 954 18
1296.2.bh \(\chi_{1296}(37, \cdot)\) n/a 840 12
1296.2.bk \(\chi_{1296}(35, \cdot)\) n/a 840 12
1296.2.bn \(\chi_{1296}(23, \cdot)\) None 0 18
1296.2.bp \(\chi_{1296}(25, \cdot)\) None 0 18
1296.2.bq \(\chi_{1296}(47, \cdot)\) n/a 972 18
1296.2.bs \(\chi_{1296}(11, \cdot)\) n/a 7704 36
1296.2.bv \(\chi_{1296}(13, \cdot)\) n/a 7704 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1296))\) into lower level spaces

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