Properties

Label 5635.2
Level 5635
Weight 2
Dimension 1082136
Nonzero newspaces 48
Sturm bound 4967424

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Defining parameters

Level: \( N \) = \( 5635 = 5 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(4967424\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5635))\).

Total New Old
Modular forms 1252416 1094360 158056
Cusp forms 1231297 1082136 149161
Eisenstein series 21119 12224 8895

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5635))\)

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
5635.2.a \(\chi_{5635}(1, \cdot)\) 5635.2.a.a 1 1
5635.2.a.b 1
5635.2.a.c 1
5635.2.a.d 1
5635.2.a.e 1
5635.2.a.f 1
5635.2.a.g 1
5635.2.a.h 1
5635.2.a.i 1
5635.2.a.j 1
5635.2.a.k 1
5635.2.a.l 1
5635.2.a.m 1
5635.2.a.n 2
5635.2.a.o 2
5635.2.a.p 2
5635.2.a.q 2
5635.2.a.r 3
5635.2.a.s 4
5635.2.a.t 4
5635.2.a.u 4
5635.2.a.v 4
5635.2.a.w 4
5635.2.a.x 5
5635.2.a.y 5
5635.2.a.z 6
5635.2.a.ba 6
5635.2.a.bb 8
5635.2.a.bc 12
5635.2.a.bd 12
5635.2.a.be 13
5635.2.a.bf 13
5635.2.a.bg 13
5635.2.a.bh 13
5635.2.a.bi 15
5635.2.a.bj 15
5635.2.a.bk 16
5635.2.a.bl 16
5635.2.a.bm 17
5635.2.a.bn 17
5635.2.a.bo 28
5635.2.a.bp 28
5635.2.c \(\chi_{5635}(4509, \cdot)\) n/a 450 1
5635.2.d \(\chi_{5635}(5634, \cdot)\) n/a 472 1
5635.2.f \(\chi_{5635}(1126, \cdot)\) n/a 320 1
5635.2.i \(\chi_{5635}(116, \cdot)\) n/a 584 2
5635.2.k \(\chi_{5635}(783, \cdot)\) n/a 880 2
5635.2.l \(\chi_{5635}(2598, \cdot)\) n/a 964 2
5635.2.p \(\chi_{5635}(1011, \cdot)\) n/a 640 2
5635.2.r \(\chi_{5635}(3449, \cdot)\) n/a 944 2
5635.2.s \(\chi_{5635}(1059, \cdot)\) n/a 880 2
5635.2.u \(\chi_{5635}(806, \cdot)\) n/a 2448 6
5635.2.v \(\chi_{5635}(246, \cdot)\) n/a 3280 10
5635.2.w \(\chi_{5635}(668, \cdot)\) n/a 1760 4
5635.2.z \(\chi_{5635}(1402, \cdot)\) n/a 1888 4
5635.2.bc \(\chi_{5635}(321, \cdot)\) n/a 2688 6
5635.2.be \(\chi_{5635}(804, \cdot)\) n/a 4008 6
5635.2.bf \(\chi_{5635}(484, \cdot)\) n/a 3696 6
5635.2.bh \(\chi_{5635}(576, \cdot)\) n/a 4944 12
5635.2.bk \(\chi_{5635}(636, \cdot)\) n/a 3200 10
5635.2.bm \(\chi_{5635}(244, \cdot)\) n/a 4720 10
5635.2.bn \(\chi_{5635}(834, \cdot)\) n/a 4820 10
5635.2.bq \(\chi_{5635}(22, \cdot)\) n/a 8016 12
5635.2.br \(\chi_{5635}(622, \cdot)\) n/a 7392 12
5635.2.bt \(\chi_{5635}(361, \cdot)\) n/a 6400 20
5635.2.bv \(\chi_{5635}(254, \cdot)\) n/a 7392 12
5635.2.bw \(\chi_{5635}(229, \cdot)\) n/a 8016 12
5635.2.by \(\chi_{5635}(206, \cdot)\) n/a 5376 12
5635.2.cc \(\chi_{5635}(148, \cdot)\) n/a 9640 20
5635.2.cd \(\chi_{5635}(48, \cdot)\) n/a 9440 20
5635.2.cg \(\chi_{5635}(324, \cdot)\) n/a 9440 20
5635.2.ch \(\chi_{5635}(19, \cdot)\) n/a 9440 20
5635.2.cj \(\chi_{5635}(166, \cdot)\) n/a 6400 20
5635.2.cm \(\chi_{5635}(36, \cdot)\) n/a 26880 60
5635.2.cn \(\chi_{5635}(137, \cdot)\) n/a 16032 24
5635.2.cq \(\chi_{5635}(47, \cdot)\) n/a 14784 24
5635.2.cr \(\chi_{5635}(67, \cdot)\) n/a 18880 40
5635.2.cu \(\chi_{5635}(117, \cdot)\) n/a 18880 40
5635.2.cw \(\chi_{5635}(29, \cdot)\) n/a 40080 60
5635.2.cx \(\chi_{5635}(34, \cdot)\) n/a 40080 60
5635.2.cz \(\chi_{5635}(76, \cdot)\) n/a 26880 60
5635.2.dc \(\chi_{5635}(16, \cdot)\) n/a 53760 120
5635.2.de \(\chi_{5635}(13, \cdot)\) n/a 80160 120
5635.2.df \(\chi_{5635}(43, \cdot)\) n/a 80160 120
5635.2.dj \(\chi_{5635}(61, \cdot)\) n/a 53760 120
5635.2.dl \(\chi_{5635}(89, \cdot)\) n/a 80160 120
5635.2.dm \(\chi_{5635}(4, \cdot)\) n/a 80160 120
5635.2.do \(\chi_{5635}(3, \cdot)\) n/a 160320 240
5635.2.dr \(\chi_{5635}(37, \cdot)\) n/a 160320 240

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5635))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5635)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(805))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1127))\)\(^{\oplus 2}\)