Properties

Label 1275.2
Level 1275
Weight 2
Dimension 38922
Nonzero newspaces 36
Sturm bound 230400
Trace bound 14

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Defining parameters

Level: \( N \) = \( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(230400\)
Trace bound: \(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1275))\).

Total New Old
Modular forms 59392 40154 19238
Cusp forms 55809 38922 16887
Eisenstein series 3583 1232 2351

Trace form

\( 38922 q + 2 q^{2} - 86 q^{3} - 158 q^{4} + 12 q^{5} - 122 q^{6} - 152 q^{7} + 42 q^{8} - 78 q^{9} + O(q^{10}) \) \( 38922 q + 2 q^{2} - 86 q^{3} - 158 q^{4} + 12 q^{5} - 122 q^{6} - 152 q^{7} + 42 q^{8} - 78 q^{9} - 188 q^{10} + 24 q^{11} - 42 q^{12} - 132 q^{13} + 80 q^{14} - 100 q^{15} - 198 q^{16} + 18 q^{17} - 174 q^{18} - 176 q^{19} - 72 q^{20} - 132 q^{21} - 208 q^{22} - 16 q^{23} - 166 q^{24} - 284 q^{25} + 84 q^{26} - 86 q^{27} - 200 q^{28} + 12 q^{29} - 156 q^{30} - 216 q^{31} + 46 q^{32} - 44 q^{33} - 60 q^{34} + 40 q^{35} - 154 q^{36} - 88 q^{37} + 64 q^{38} - 112 q^{39} - 260 q^{40} + 84 q^{41} - 236 q^{42} - 176 q^{43} - 32 q^{44} - 256 q^{45} - 328 q^{46} - 32 q^{47} - 294 q^{48} - 302 q^{49} - 212 q^{50} - 378 q^{51} - 612 q^{52} - 88 q^{53} - 350 q^{54} - 264 q^{55} + 80 q^{56} - 204 q^{57} - 148 q^{58} + 8 q^{59} - 156 q^{60} - 132 q^{61} + 104 q^{62} + 24 q^{63} - 358 q^{64} + 116 q^{65} + 28 q^{66} + 96 q^{67} + 130 q^{68} - 16 q^{69} - 232 q^{70} - 48 q^{71} + 142 q^{72} - 420 q^{73} - 140 q^{74} - 28 q^{75} - 1192 q^{76} - 160 q^{77} - 212 q^{78} - 392 q^{79} - 332 q^{80} + 10 q^{81} - 988 q^{82} - 216 q^{83} - 620 q^{84} - 678 q^{85} - 440 q^{86} - 460 q^{87} - 1680 q^{88} - 480 q^{89} - 112 q^{90} - 1032 q^{91} - 1184 q^{92} - 528 q^{93} - 1448 q^{94} - 368 q^{95} - 786 q^{96} - 972 q^{97} - 694 q^{98} - 264 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1275))\)

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
1275.2.a \(\chi_{1275}(1, \cdot)\) 1275.2.a.a 1 1
1275.2.a.b 1
1275.2.a.c 1
1275.2.a.d 1
1275.2.a.e 1
1275.2.a.f 1
1275.2.a.g 1
1275.2.a.h 2
1275.2.a.i 2
1275.2.a.j 2
1275.2.a.k 2
1275.2.a.l 2
1275.2.a.m 2
1275.2.a.n 2
1275.2.a.o 3
1275.2.a.p 3
1275.2.a.q 3
1275.2.a.r 3
1275.2.a.s 3
1275.2.a.t 4
1275.2.a.u 5
1275.2.a.v 5
1275.2.b \(\chi_{1275}(1174, \cdot)\) 1275.2.b.a 2 1
1275.2.b.b 2
1275.2.b.c 2
1275.2.b.d 4
1275.2.b.e 4
1275.2.b.f 4
1275.2.b.g 4
1275.2.b.h 6
1275.2.b.i 6
1275.2.b.j 6
1275.2.b.k 8
1275.2.d \(\chi_{1275}(424, \cdot)\) 1275.2.d.a 2 1
1275.2.d.b 2
1275.2.d.c 2
1275.2.d.d 2
1275.2.d.e 4
1275.2.d.f 4
1275.2.d.g 8
1275.2.d.h 8
1275.2.d.i 12
1275.2.d.j 12
1275.2.g \(\chi_{1275}(526, \cdot)\) 1275.2.g.a 2 1
1275.2.g.b 2
1275.2.g.c 4
1275.2.g.d 8
1275.2.g.e 12
1275.2.g.f 12
1275.2.g.g 16
1275.2.j \(\chi_{1275}(676, \cdot)\) n/a 112 2
1275.2.k \(\chi_{1275}(1007, \cdot)\) n/a 208 2
1275.2.m \(\chi_{1275}(443, \cdot)\) n/a 192 2
1275.2.o \(\chi_{1275}(407, \cdot)\) n/a 208 2
1275.2.r \(\chi_{1275}(293, \cdot)\) n/a 208 2
1275.2.s \(\chi_{1275}(574, \cdot)\) n/a 112 2
1275.2.u \(\chi_{1275}(256, \cdot)\) n/a 320 4
1275.2.w \(\chi_{1275}(332, \cdot)\) n/a 416 4
1275.2.x \(\chi_{1275}(76, \cdot)\) n/a 232 4
1275.2.ba \(\chi_{1275}(49, \cdot)\) n/a 208 4
1275.2.bb \(\chi_{1275}(32, \cdot)\) n/a 416 4
1275.2.bd \(\chi_{1275}(16, \cdot)\) n/a 368 4
1275.2.bh \(\chi_{1275}(154, \cdot)\) n/a 320 4
1275.2.bj \(\chi_{1275}(169, \cdot)\) n/a 352 4
1275.2.bl \(\chi_{1275}(7, \cdot)\) n/a 432 8
1275.2.bm \(\chi_{1275}(74, \cdot)\) n/a 832 8
1275.2.bo \(\chi_{1275}(176, \cdot)\) n/a 864 8
1275.2.bq \(\chi_{1275}(82, \cdot)\) n/a 432 8
1275.2.bt \(\chi_{1275}(4, \cdot)\) n/a 704 8
1275.2.bv \(\chi_{1275}(98, \cdot)\) n/a 1408 8
1275.2.bw \(\chi_{1275}(152, \cdot)\) n/a 1408 8
1275.2.by \(\chi_{1275}(137, \cdot)\) n/a 1280 8
1275.2.ca \(\chi_{1275}(38, \cdot)\) n/a 1408 8
1275.2.cc \(\chi_{1275}(106, \cdot)\) n/a 736 8
1275.2.ce \(\chi_{1275}(2, \cdot)\) n/a 2816 16
1275.2.cg \(\chi_{1275}(19, \cdot)\) n/a 1472 16
1275.2.cj \(\chi_{1275}(121, \cdot)\) n/a 1408 16
1275.2.cl \(\chi_{1275}(53, \cdot)\) n/a 2816 16
1275.2.cn \(\chi_{1275}(22, \cdot)\) n/a 2880 32
1275.2.cp \(\chi_{1275}(11, \cdot)\) n/a 5632 32
1275.2.cr \(\chi_{1275}(14, \cdot)\) n/a 5632 32
1275.2.cs \(\chi_{1275}(73, \cdot)\) n/a 2880 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1275))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1275)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 2}\)