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Properties

Label 4158.2
Level 4158
Weight 2
Dimension 115800
Nonzero newspaces 64
Sturm bound 1866240

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Defining parameters

Level: \( N \) = \( 4158 = 2 \cdot 3^{3} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(1866240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4158))\).

Total New Old
Modular forms 473760 115800 357960
Cusp forms 459361 115800 343561
Eisenstein series 14399 0 14399

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4158))\)

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
4158.2.a \(\chi_{4158}(1, \cdot)\) 4158.2.a.a 1 1
4158.2.a.b 1
4158.2.a.c 1
4158.2.a.d 1
4158.2.a.e 1
4158.2.a.f 1
4158.2.a.g 1
4158.2.a.h 1
4158.2.a.i 1
4158.2.a.j 1
4158.2.a.k 1
4158.2.a.l 1
4158.2.a.m 1
4158.2.a.n 1
4158.2.a.o 1
4158.2.a.p 1
4158.2.a.q 1
4158.2.a.r 1
4158.2.a.s 1
4158.2.a.t 1
4158.2.a.u 1
4158.2.a.v 1
4158.2.a.w 1
4158.2.a.x 1
4158.2.a.y 1
4158.2.a.z 1
4158.2.a.ba 1
4158.2.a.bb 1
4158.2.a.bc 2
4158.2.a.bd 2
4158.2.a.be 2
4158.2.a.bf 2
4158.2.a.bg 2
4158.2.a.bh 2
4158.2.a.bi 2
4158.2.a.bj 2
4158.2.a.bk 2
4158.2.a.bl 2
4158.2.a.bm 2
4158.2.a.bn 2
4158.2.a.bo 2
4158.2.a.bp 2
4158.2.a.bq 3
4158.2.a.br 3
4158.2.a.bs 3
4158.2.a.bt 3
4158.2.a.bu 3
4158.2.a.bv 3
4158.2.a.bw 3
4158.2.a.bx 3
4158.2.c \(\chi_{4158}(2969, \cdot)\) 4158.2.c.a 24 1
4158.2.c.b 24
4158.2.c.c 24
4158.2.c.d 24
4158.2.e \(\chi_{4158}(3079, \cdot)\) n/a 128 1
4158.2.g \(\chi_{4158}(2267, \cdot)\) n/a 104 1
4158.2.i \(\chi_{4158}(793, \cdot)\) n/a 160 2
4158.2.j \(\chi_{4158}(1387, \cdot)\) n/a 120 2
4158.2.k \(\chi_{4158}(2377, \cdot)\) n/a 216 2
4158.2.l \(\chi_{4158}(2179, \cdot)\) n/a 160 2
4158.2.m \(\chi_{4158}(379, \cdot)\) n/a 384 4
4158.2.n \(\chi_{4158}(2089, \cdot)\) n/a 192 2
4158.2.p \(\chi_{4158}(3761, \cdot)\) n/a 192 2
4158.2.r \(\chi_{4158}(2861, \cdot)\) n/a 216 2
4158.2.w \(\chi_{4158}(1277, \cdot)\) n/a 160 2
4158.2.y \(\chi_{4158}(881, \cdot)\) n/a 160 2
4158.2.ba \(\chi_{4158}(1187, \cdot)\) n/a 256 2
4158.2.bd \(\chi_{4158}(901, \cdot)\) n/a 192 2
4158.2.bf \(\chi_{4158}(307, \cdot)\) n/a 192 2
4158.2.bh \(\chi_{4158}(989, \cdot)\) n/a 192 2
4158.2.bj \(\chi_{4158}(197, \cdot)\) n/a 144 2
4158.2.bk \(\chi_{4158}(703, \cdot)\) n/a 256 2
4158.2.bn \(\chi_{4158}(89, \cdot)\) n/a 160 2
4158.2.bp \(\chi_{4158}(463, \cdot)\) n/a 1080 6
4158.2.bq \(\chi_{4158}(67, \cdot)\) n/a 1440 6
4158.2.br \(\chi_{4158}(529, \cdot)\) n/a 1440 6
4158.2.bt \(\chi_{4158}(377, \cdot)\) n/a 512 4
4158.2.bv \(\chi_{4158}(811, \cdot)\) n/a 512 4
4158.2.bx \(\chi_{4158}(701, \cdot)\) n/a 384 4
4158.2.bz \(\chi_{4158}(289, \cdot)\) n/a 768 8
4158.2.ca \(\chi_{4158}(163, \cdot)\) n/a 1024 8
4158.2.cb \(\chi_{4158}(631, \cdot)\) n/a 576 8
4158.2.cc \(\chi_{4158}(37, \cdot)\) n/a 768 8
4158.2.ch \(\chi_{4158}(769, \cdot)\) n/a 1728 6
4158.2.ci \(\chi_{4158}(439, \cdot)\) n/a 1728 6
4158.2.cj \(\chi_{4158}(419, \cdot)\) n/a 1440 6
4158.2.ck \(\chi_{4158}(659, \cdot)\) n/a 1296 6
4158.2.cl \(\chi_{4158}(551, \cdot)\) n/a 1440 6
4158.2.cm \(\chi_{4158}(65, \cdot)\) n/a 1728 6
4158.2.cv \(\chi_{4158}(263, \cdot)\) n/a 1728 6
4158.2.cw \(\chi_{4158}(353, \cdot)\) n/a 1440 6
4158.2.cx \(\chi_{4158}(241, \cdot)\) n/a 1728 6
4158.2.cz \(\chi_{4158}(467, \cdot)\) n/a 768 8
4158.2.dc \(\chi_{4158}(271, \cdot)\) n/a 1024 8
4158.2.dd \(\chi_{4158}(827, \cdot)\) n/a 576 8
4158.2.df \(\chi_{4158}(233, \cdot)\) n/a 768 8
4158.2.dh \(\chi_{4158}(937, \cdot)\) n/a 768 8
4158.2.dj \(\chi_{4158}(73, \cdot)\) n/a 768 8
4158.2.dm \(\chi_{4158}(107, \cdot)\) n/a 1024 8
4158.2.do \(\chi_{4158}(125, \cdot)\) n/a 768 8
4158.2.dq \(\chi_{4158}(521, \cdot)\) n/a 768 8
4158.2.dv \(\chi_{4158}(269, \cdot)\) n/a 1024 8
4158.2.dx \(\chi_{4158}(359, \cdot)\) n/a 768 8
4158.2.dz \(\chi_{4158}(19, \cdot)\) n/a 768 8
4158.2.ea \(\chi_{4158}(25, \cdot)\) n/a 6912 24
4158.2.eb \(\chi_{4158}(445, \cdot)\) n/a 6912 24
4158.2.ec \(\chi_{4158}(169, \cdot)\) n/a 5184 24
4158.2.ed \(\chi_{4158}(481, \cdot)\) n/a 6912 24
4158.2.ee \(\chi_{4158}(149, \cdot)\) n/a 6912 24
4158.2.ef \(\chi_{4158}(5, \cdot)\) n/a 6912 24
4158.2.eo \(\chi_{4158}(47, \cdot)\) n/a 6912 24
4158.2.ep \(\chi_{4158}(95, \cdot)\) n/a 6912 24
4158.2.eq \(\chi_{4158}(335, \cdot)\) n/a 6912 24
4158.2.er \(\chi_{4158}(29, \cdot)\) n/a 5184 24
4158.2.es \(\chi_{4158}(61, \cdot)\) n/a 6912 24
4158.2.et \(\chi_{4158}(13, \cdot)\) n/a 6912 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4158))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4158)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(594))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(693))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1386))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2079))\)\(^{\oplus 2}\)