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Properties

Label 1792.2
Level 1792
Weight 2
Dimension 52472
Nonzero newspaces 24
Sturm bound 393216
Trace bound 193

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Defining parameters

Level: \( N \) = \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(393216\)
Trace bound: \(193\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1792))\).

Total New Old
Modular forms 100416 53512 46904
Cusp forms 96193 52472 43721
Eisenstein series 4223 1040 3183

Trace form

\( 52472 q - 128 q^{2} - 96 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 120 q^{7} - 320 q^{8} - 160 q^{9} + O(q^{10}) \) \( 52472 q - 128 q^{2} - 96 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 120 q^{7} - 320 q^{8} - 160 q^{9} - 128 q^{10} - 96 q^{11} - 128 q^{12} - 128 q^{13} - 160 q^{14} - 240 q^{15} - 128 q^{16} - 192 q^{17} - 128 q^{18} - 96 q^{19} - 128 q^{20} - 160 q^{21} - 320 q^{22} - 96 q^{23} - 128 q^{24} - 160 q^{25} - 128 q^{26} - 96 q^{27} - 160 q^{28} - 320 q^{29} - 128 q^{30} - 80 q^{31} - 128 q^{32} - 224 q^{33} - 128 q^{34} - 120 q^{35} - 320 q^{36} - 128 q^{37} - 128 q^{38} - 96 q^{39} - 128 q^{40} - 160 q^{41} - 160 q^{42} - 240 q^{43} - 128 q^{44} - 80 q^{45} - 128 q^{46} - 96 q^{47} - 128 q^{48} - 240 q^{49} - 320 q^{50} - 32 q^{51} - 128 q^{52} - 64 q^{53} - 128 q^{54} + 32 q^{55} - 160 q^{56} - 272 q^{57} - 128 q^{58} + 32 q^{59} - 128 q^{60} - 128 q^{62} - 48 q^{63} - 320 q^{64} - 160 q^{65} - 128 q^{66} + 64 q^{67} - 128 q^{68} - 160 q^{70} - 112 q^{71} - 128 q^{72} - 32 q^{73} - 128 q^{74} + 32 q^{75} - 128 q^{76} - 128 q^{77} - 320 q^{78} - 32 q^{79} - 128 q^{80} - 120 q^{81} - 128 q^{82} - 96 q^{83} - 160 q^{84} - 240 q^{85} - 128 q^{86} - 96 q^{87} - 128 q^{88} - 160 q^{89} - 128 q^{90} - 120 q^{91} - 320 q^{92} - 224 q^{93} - 128 q^{94} - 80 q^{95} - 128 q^{96} - 224 q^{97} - 160 q^{98} - 192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1792))\)

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
1792.2.a \(\chi_{1792}(1, \cdot)\) 1792.2.a.a 1 1
1792.2.a.b 1
1792.2.a.c 1
1792.2.a.d 1
1792.2.a.e 1
1792.2.a.f 1
1792.2.a.g 1
1792.2.a.h 1
1792.2.a.i 2
1792.2.a.j 2
1792.2.a.k 2
1792.2.a.l 2
1792.2.a.m 2
1792.2.a.n 2
1792.2.a.o 2
1792.2.a.p 2
1792.2.a.q 2
1792.2.a.r 2
1792.2.a.s 2
1792.2.a.t 2
1792.2.a.u 4
1792.2.a.v 4
1792.2.a.w 4
1792.2.a.x 4
1792.2.b \(\chi_{1792}(897, \cdot)\) 1792.2.b.a 2 1
1792.2.b.b 2
1792.2.b.c 2
1792.2.b.d 2
1792.2.b.e 2
1792.2.b.f 2
1792.2.b.g 2
1792.2.b.h 2
1792.2.b.i 2
1792.2.b.j 2
1792.2.b.k 4
1792.2.b.l 4
1792.2.b.m 4
1792.2.b.n 4
1792.2.b.o 6
1792.2.b.p 6
1792.2.e \(\chi_{1792}(895, \cdot)\) 1792.2.e.a 4 1
1792.2.e.b 4
1792.2.e.c 4
1792.2.e.d 8
1792.2.e.e 8
1792.2.e.f 8
1792.2.e.g 8
1792.2.e.h 8
1792.2.e.i 8
1792.2.f \(\chi_{1792}(1791, \cdot)\) 1792.2.f.a 4 1
1792.2.f.b 4
1792.2.f.c 4
1792.2.f.d 4
1792.2.f.e 4
1792.2.f.f 4
1792.2.f.g 4
1792.2.f.h 4
1792.2.f.i 4
1792.2.f.j 8
1792.2.f.k 8
1792.2.f.l 8
1792.2.i \(\chi_{1792}(513, \cdot)\) n/a 120 2
1792.2.j \(\chi_{1792}(447, \cdot)\) n/a 128 2
1792.2.m \(\chi_{1792}(449, \cdot)\) 1792.2.m.a 8 2
1792.2.m.b 8
1792.2.m.c 8
1792.2.m.d 8
1792.2.m.e 16
1792.2.m.f 16
1792.2.m.g 16
1792.2.m.h 16
1792.2.p \(\chi_{1792}(255, \cdot)\) n/a 120 2
1792.2.q \(\chi_{1792}(383, \cdot)\) n/a 120 2
1792.2.t \(\chi_{1792}(641, \cdot)\) n/a 120 2
1792.2.u \(\chi_{1792}(225, \cdot)\) n/a 192 4
1792.2.x \(\chi_{1792}(223, \cdot)\) n/a 240 4
1792.2.z \(\chi_{1792}(703, \cdot)\) n/a 256 4
1792.2.ba \(\chi_{1792}(65, \cdot)\) n/a 256 4
1792.2.bc \(\chi_{1792}(113, \cdot)\) n/a 384 8
1792.2.bd \(\chi_{1792}(111, \cdot)\) n/a 496 8
1792.2.bh \(\chi_{1792}(289, \cdot)\) n/a 480 8
1792.2.bi \(\chi_{1792}(31, \cdot)\) n/a 480 8
1792.2.bk \(\chi_{1792}(55, \cdot)\) None 0 16
1792.2.bn \(\chi_{1792}(57, \cdot)\) None 0 16
1792.2.bq \(\chi_{1792}(47, \cdot)\) n/a 992 16
1792.2.br \(\chi_{1792}(81, \cdot)\) n/a 992 16
1792.2.bs \(\chi_{1792}(29, \cdot)\) n/a 6144 32
1792.2.bv \(\chi_{1792}(27, \cdot)\) n/a 8128 32
1792.2.bx \(\chi_{1792}(87, \cdot)\) None 0 32
1792.2.by \(\chi_{1792}(9, \cdot)\) None 0 32
1792.2.cb \(\chi_{1792}(37, \cdot)\) n/a 16256 64
1792.2.cc \(\chi_{1792}(3, \cdot)\) n/a 16256 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1792))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1792)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(896))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1792))\)\(^{\oplus 1}\)