Properties

Label 2775.2
Level 2775
Weight 2
Dimension 187412
Nonzero newspaces 60
Sturm bound 1094400
Trace bound 8

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Defining parameters

Level: \( N \) = \( 2775 = 3 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(1094400\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2775))\).

Total New Old
Modular forms 277632 190284 87348
Cusp forms 269569 187412 82157
Eisenstein series 8063 2872 5191

Trace form

\( 187412 q + 2 q^{2} - 216 q^{3} - 418 q^{4} + 12 q^{5} - 332 q^{6} - 412 q^{7} + 42 q^{8} - 208 q^{9} - 508 q^{10} + 8 q^{11} - 196 q^{12} - 408 q^{13} + 48 q^{14} - 260 q^{15} - 690 q^{16} + 4 q^{17} - 232 q^{18}+ \cdots - 316 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2775))\)

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
2775.2.a \(\chi_{2775}(1, \cdot)\) 2775.2.a.a 1 1
2775.2.a.b 1
2775.2.a.c 1
2775.2.a.d 1
2775.2.a.e 1
2775.2.a.f 1
2775.2.a.g 1
2775.2.a.h 1
2775.2.a.i 1
2775.2.a.j 1
2775.2.a.k 2
2775.2.a.l 2
2775.2.a.m 2
2775.2.a.n 2
2775.2.a.o 2
2775.2.a.p 2
2775.2.a.q 2
2775.2.a.r 3
2775.2.a.s 3
2775.2.a.t 3
2775.2.a.u 3
2775.2.a.v 3
2775.2.a.w 4
2775.2.a.x 4
2775.2.a.y 4
2775.2.a.z 5
2775.2.a.ba 5
2775.2.a.bb 5
2775.2.a.bc 5
2775.2.a.bd 5
2775.2.a.be 6
2775.2.a.bf 6
2775.2.a.bg 13
2775.2.a.bh 13
2775.2.c \(\chi_{2775}(1999, \cdot)\) n/a 108 1
2775.2.e \(\chi_{2775}(2626, \cdot)\) n/a 122 1
2775.2.g \(\chi_{2775}(1849, \cdot)\) n/a 112 1
2775.2.i \(\chi_{2775}(676, \cdot)\) n/a 240 2
2775.2.j \(\chi_{2775}(43, \cdot)\) n/a 228 2
2775.2.m \(\chi_{2775}(524, \cdot)\) n/a 448 2
2775.2.n \(\chi_{2775}(332, \cdot)\) n/a 448 2
2775.2.o \(\chi_{2775}(482, \cdot)\) n/a 432 2
2775.2.s \(\chi_{2775}(401, \cdot)\) n/a 468 2
2775.2.t \(\chi_{2775}(1918, \cdot)\) n/a 228 2
2775.2.v \(\chi_{2775}(556, \cdot)\) n/a 720 4
2775.2.y \(\chi_{2775}(1174, \cdot)\) n/a 224 2
2775.2.ba \(\chi_{2775}(751, \cdot)\) n/a 244 2
2775.2.bc \(\chi_{2775}(1099, \cdot)\) n/a 232 2
2775.2.bd \(\chi_{2775}(451, \cdot)\) n/a 714 6
2775.2.be \(\chi_{2775}(184, \cdot)\) n/a 768 4
2775.2.bh \(\chi_{2775}(334, \cdot)\) n/a 720 4
2775.2.bj \(\chi_{2775}(406, \cdot)\) n/a 752 4
2775.2.bl \(\chi_{2775}(82, \cdot)\) n/a 456 4
2775.2.bo \(\chi_{2775}(251, \cdot)\) n/a 936 4
2775.2.bp \(\chi_{2775}(1232, \cdot)\) n/a 896 4
2775.2.bq \(\chi_{2775}(1157, \cdot)\) n/a 896 4
2775.2.bu \(\chi_{2775}(674, \cdot)\) n/a 896 4
2775.2.bv \(\chi_{2775}(193, \cdot)\) n/a 456 4
2775.2.bx \(\chi_{2775}(121, \cdot)\) n/a 1536 8
2775.2.by \(\chi_{2775}(724, \cdot)\) n/a 672 6
2775.2.cb \(\chi_{2775}(49, \cdot)\) n/a 696 6
2775.2.cc \(\chi_{2775}(151, \cdot)\) n/a 726 6
2775.2.cg \(\chi_{2775}(253, \cdot)\) n/a 1520 8
2775.2.ch \(\chi_{2775}(179, \cdot)\) n/a 3008 8
2775.2.cl \(\chi_{2775}(38, \cdot)\) n/a 2880 8
2775.2.cm \(\chi_{2775}(887, \cdot)\) n/a 3008 8
2775.2.cn \(\chi_{2775}(191, \cdot)\) n/a 3008 8
2775.2.cq \(\chi_{2775}(142, \cdot)\) n/a 1520 8
2775.2.cr \(\chi_{2775}(196, \cdot)\) n/a 1504 8
2775.2.ct \(\chi_{2775}(454, \cdot)\) n/a 1504 8
2775.2.cw \(\chi_{2775}(64, \cdot)\) n/a 1536 8
2775.2.cz \(\chi_{2775}(457, \cdot)\) n/a 1368 12
2775.2.db \(\chi_{2775}(476, \cdot)\) n/a 2820 12
2775.2.dc \(\chi_{2775}(224, \cdot)\) n/a 2688 12
2775.2.de \(\chi_{2775}(107, \cdot)\) n/a 2688 12
2775.2.dh \(\chi_{2775}(632, \cdot)\) n/a 2688 12
2775.2.dj \(\chi_{2775}(568, \cdot)\) n/a 1368 12
2775.2.dk \(\chi_{2775}(16, \cdot)\) n/a 4608 24
2775.2.dm \(\chi_{2775}(208, \cdot)\) n/a 3040 16
2775.2.dn \(\chi_{2775}(236, \cdot)\) n/a 6016 16
2775.2.dr \(\chi_{2775}(47, \cdot)\) n/a 6016 16
2775.2.ds \(\chi_{2775}(122, \cdot)\) n/a 6016 16
2775.2.dt \(\chi_{2775}(14, \cdot)\) n/a 6016 16
2775.2.dw \(\chi_{2775}(88, \cdot)\) n/a 3040 16
2775.2.dz \(\chi_{2775}(136, \cdot)\) n/a 4512 24
2775.2.ea \(\chi_{2775}(34, \cdot)\) n/a 4512 24
2775.2.ed \(\chi_{2775}(4, \cdot)\) n/a 4608 24
2775.2.ee \(\chi_{2775}(13, \cdot)\) n/a 9120 48
2775.2.eg \(\chi_{2775}(62, \cdot)\) n/a 18048 48
2775.2.ej \(\chi_{2775}(53, \cdot)\) n/a 18048 48
2775.2.el \(\chi_{2775}(59, \cdot)\) n/a 18048 48
2775.2.em \(\chi_{2775}(56, \cdot)\) n/a 18048 48
2775.2.eo \(\chi_{2775}(22, \cdot)\) n/a 9120 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2775))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2775)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(555))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(925))\)\(^{\oplus 2}\)