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Properties

Label 1395.2
Level 1395
Weight 2
Dimension 49272
Nonzero newspaces 60
Sturm bound 276480
Trace bound 18

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Defining parameters

Level: \( N \) = \( 1395 = 3^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(276480\)
Trace bound: \(18\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1395))\).

Total New Old
Modular forms 71040 50840 20200
Cusp forms 67201 49272 17929
Eisenstein series 3839 1568 2271

Trace form

\( 49272 q - 76 q^{2} - 104 q^{3} - 68 q^{4} - 117 q^{5} - 328 q^{6} - 66 q^{7} - 84 q^{8} - 112 q^{9} - 375 q^{10} - 262 q^{11} - 136 q^{12} - 86 q^{13} - 114 q^{14} - 188 q^{15} - 256 q^{16} - 94 q^{17}+ \cdots - 380 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1395))\)

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
1395.2.a \(\chi_{1395}(1, \cdot)\) 1395.2.a.a 1 1
1395.2.a.b 1
1395.2.a.c 1
1395.2.a.d 1
1395.2.a.e 1
1395.2.a.f 2
1395.2.a.g 2
1395.2.a.h 3
1395.2.a.i 3
1395.2.a.j 3
1395.2.a.k 4
1395.2.a.l 4
1395.2.a.m 4
1395.2.a.n 5
1395.2.a.o 5
1395.2.a.p 5
1395.2.a.q 5
1395.2.c \(\chi_{1395}(559, \cdot)\) 1395.2.c.a 2 1
1395.2.c.b 2
1395.2.c.c 4
1395.2.c.d 8
1395.2.c.e 10
1395.2.c.f 10
1395.2.c.g 16
1395.2.c.h 22
1395.2.e \(\chi_{1395}(836, \cdot)\) 1395.2.e.a 40 1
1395.2.g \(\chi_{1395}(1394, \cdot)\) 1395.2.g.a 24 1
1395.2.g.b 40
1395.2.i \(\chi_{1395}(466, \cdot)\) n/a 240 2
1395.2.j \(\chi_{1395}(211, \cdot)\) n/a 256 2
1395.2.k \(\chi_{1395}(346, \cdot)\) n/a 256 2
1395.2.l \(\chi_{1395}(676, \cdot)\) n/a 108 2
1395.2.m \(\chi_{1395}(433, \cdot)\) n/a 156 2
1395.2.n \(\chi_{1395}(683, \cdot)\) n/a 120 2
1395.2.q \(\chi_{1395}(721, \cdot)\) n/a 208 4
1395.2.r \(\chi_{1395}(26, \cdot)\) 1395.2.r.a 88 2
1395.2.t \(\chi_{1395}(1234, \cdot)\) n/a 156 2
1395.2.v \(\chi_{1395}(254, \cdot)\) n/a 376 2
1395.2.ba \(\chi_{1395}(464, \cdot)\) n/a 376 2
1395.2.bc \(\chi_{1395}(119, \cdot)\) n/a 376 2
1395.2.be \(\chi_{1395}(304, \cdot)\) n/a 376 2
1395.2.bh \(\chi_{1395}(371, \cdot)\) n/a 256 2
1395.2.bj \(\chi_{1395}(626, \cdot)\) n/a 256 2
1395.2.bl \(\chi_{1395}(94, \cdot)\) n/a 360 2
1395.2.bn \(\chi_{1395}(439, \cdot)\) n/a 376 2
1395.2.bo \(\chi_{1395}(491, \cdot)\) n/a 256 2
1395.2.br \(\chi_{1395}(584, \cdot)\) n/a 128 2
1395.2.bu \(\chi_{1395}(89, \cdot)\) n/a 256 4
1395.2.bw \(\chi_{1395}(116, \cdot)\) n/a 160 4
1395.2.by \(\chi_{1395}(64, \cdot)\) n/a 312 4
1395.2.cc \(\chi_{1395}(98, \cdot)\) n/a 256 4
1395.2.cd \(\chi_{1395}(37, \cdot)\) n/a 312 4
1395.2.ce \(\chi_{1395}(88, \cdot)\) n/a 752 4
1395.2.cf \(\chi_{1395}(428, \cdot)\) n/a 752 4
1395.2.ck \(\chi_{1395}(32, \cdot)\) n/a 720 4
1395.2.cl \(\chi_{1395}(563, \cdot)\) n/a 752 4
1395.2.cm \(\chi_{1395}(247, \cdot)\) n/a 752 4
1395.2.cn \(\chi_{1395}(223, \cdot)\) n/a 752 4
1395.2.cq \(\chi_{1395}(226, \cdot)\) n/a 432 8
1395.2.cr \(\chi_{1395}(286, \cdot)\) n/a 1024 8
1395.2.cs \(\chi_{1395}(76, \cdot)\) n/a 1024 8
1395.2.ct \(\chi_{1395}(16, \cdot)\) n/a 1024 8
1395.2.cw \(\chi_{1395}(8, \cdot)\) n/a 512 8
1395.2.cx \(\chi_{1395}(523, \cdot)\) n/a 624 8
1395.2.cz \(\chi_{1395}(44, \cdot)\) n/a 512 8
1395.2.dc \(\chi_{1395}(176, \cdot)\) n/a 1024 8
1395.2.dd \(\chi_{1395}(634, \cdot)\) n/a 1504 8
1395.2.df \(\chi_{1395}(4, \cdot)\) n/a 1504 8
1395.2.dh \(\chi_{1395}(11, \cdot)\) n/a 1024 8
1395.2.dj \(\chi_{1395}(356, \cdot)\) n/a 1024 8
1395.2.dm \(\chi_{1395}(49, \cdot)\) n/a 1504 8
1395.2.do \(\chi_{1395}(569, \cdot)\) n/a 1504 8
1395.2.dq \(\chi_{1395}(29, \cdot)\) n/a 1504 8
1395.2.dv \(\chi_{1395}(74, \cdot)\) n/a 1504 8
1395.2.dx \(\chi_{1395}(19, \cdot)\) n/a 624 8
1395.2.dz \(\chi_{1395}(251, \cdot)\) n/a 352 8
1395.2.ec \(\chi_{1395}(13, \cdot)\) n/a 3008 16
1395.2.ed \(\chi_{1395}(58, \cdot)\) n/a 3008 16
1395.2.ee \(\chi_{1395}(38, \cdot)\) n/a 3008 16
1395.2.ef \(\chi_{1395}(2, \cdot)\) n/a 3008 16
1395.2.ek \(\chi_{1395}(173, \cdot)\) n/a 3008 16
1395.2.el \(\chi_{1395}(52, \cdot)\) n/a 3008 16
1395.2.em \(\chi_{1395}(73, \cdot)\) n/a 1248 16
1395.2.en \(\chi_{1395}(107, \cdot)\) n/a 1024 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1395))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1395)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(279))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(465))\)\(^{\oplus 2}\)