Properties

Label 1275.4
Level 1275
Weight 4
Dimension 118004
Nonzero newspaces 36
Sturm bound 460800
Trace bound 14

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Defining parameters

Level: \( N \) = \( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(460800\)
Trace bound: \(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1275))\).

Total New Old
Modular forms 174592 119236 55356
Cusp forms 171008 118004 53004
Eisenstein series 3584 1232 2352

Trace form

\( 118004 q + 16 q^{2} - 108 q^{3} - 264 q^{4} + 12 q^{5} - 132 q^{6} - 248 q^{7} - 144 q^{8} - 156 q^{9} - 408 q^{10} + 444 q^{12} + 424 q^{13} + 736 q^{14} + 240 q^{15} - 952 q^{16} - 816 q^{17} - 1812 q^{18}+ \cdots + 848 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1275))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1275.4.a \(\chi_{1275}(1, \cdot)\) 1275.4.a.a 1 1
1275.4.a.b 1
1275.4.a.c 1
1275.4.a.d 1
1275.4.a.e 1
1275.4.a.f 1
1275.4.a.g 1
1275.4.a.h 1
1275.4.a.i 1
1275.4.a.j 1
1275.4.a.k 1
1275.4.a.l 2
1275.4.a.m 2
1275.4.a.n 2
1275.4.a.o 2
1275.4.a.p 2
1275.4.a.q 3
1275.4.a.r 5
1275.4.a.s 5
1275.4.a.t 5
1275.4.a.u 5
1275.4.a.v 6
1275.4.a.w 6
1275.4.a.x 7
1275.4.a.y 7
1275.4.a.z 8
1275.4.a.ba 8
1275.4.a.bb 9
1275.4.a.bc 9
1275.4.a.bd 10
1275.4.a.be 10
1275.4.a.bf 14
1275.4.a.bg 14
1275.4.b \(\chi_{1275}(1174, \cdot)\) n/a 144 1
1275.4.d \(\chi_{1275}(424, \cdot)\) n/a 160 1
1275.4.g \(\chi_{1275}(526, \cdot)\) n/a 172 1
1275.4.j \(\chi_{1275}(676, \cdot)\) n/a 344 2
1275.4.k \(\chi_{1275}(1007, \cdot)\) n/a 640 2
1275.4.m \(\chi_{1275}(443, \cdot)\) n/a 576 2
1275.4.o \(\chi_{1275}(407, \cdot)\) n/a 640 2
1275.4.r \(\chi_{1275}(293, \cdot)\) n/a 640 2
1275.4.s \(\chi_{1275}(574, \cdot)\) n/a 320 2
1275.4.u \(\chi_{1275}(256, \cdot)\) n/a 960 4
1275.4.w \(\chi_{1275}(332, \cdot)\) n/a 1280 4
1275.4.x \(\chi_{1275}(76, \cdot)\) n/a 680 4
1275.4.ba \(\chi_{1275}(49, \cdot)\) n/a 656 4
1275.4.bb \(\chi_{1275}(32, \cdot)\) n/a 1280 4
1275.4.bd \(\chi_{1275}(16, \cdot)\) n/a 1072 4
1275.4.bh \(\chi_{1275}(154, \cdot)\) n/a 960 4
1275.4.bj \(\chi_{1275}(169, \cdot)\) n/a 1088 4
1275.4.bl \(\chi_{1275}(7, \cdot)\) n/a 1296 8
1275.4.bm \(\chi_{1275}(74, \cdot)\) n/a 2560 8
1275.4.bo \(\chi_{1275}(176, \cdot)\) n/a 2688 8
1275.4.bq \(\chi_{1275}(82, \cdot)\) n/a 1296 8
1275.4.bt \(\chi_{1275}(4, \cdot)\) n/a 2176 8
1275.4.bv \(\chi_{1275}(98, \cdot)\) n/a 4288 8
1275.4.bw \(\chi_{1275}(152, \cdot)\) n/a 4288 8
1275.4.by \(\chi_{1275}(137, \cdot)\) n/a 3840 8
1275.4.ca \(\chi_{1275}(38, \cdot)\) n/a 4288 8
1275.4.cc \(\chi_{1275}(106, \cdot)\) n/a 2144 8
1275.4.ce \(\chi_{1275}(2, \cdot)\) n/a 8576 16
1275.4.cg \(\chi_{1275}(19, \cdot)\) n/a 4288 16
1275.4.cj \(\chi_{1275}(121, \cdot)\) n/a 4352 16
1275.4.cl \(\chi_{1275}(53, \cdot)\) n/a 8576 16
1275.4.cn \(\chi_{1275}(22, \cdot)\) n/a 8640 32
1275.4.cp \(\chi_{1275}(11, \cdot)\) n/a 17152 32
1275.4.cr \(\chi_{1275}(14, \cdot)\) n/a 17152 32
1275.4.cs \(\chi_{1275}(73, \cdot)\) n/a 8640 32

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1275))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1275)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1275))\)\(^{\oplus 1}\)