Properties

Label 4140.3
Level 4140
Weight 3
Dimension 383632
Nonzero newspaces 48
Sturm bound 2737152

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Defining parameters

Level: \( N \) = \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(2737152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(4140))\).

Total New Old
Modular forms 919424 385904 533520
Cusp forms 905344 383632 521712
Eisenstein series 14080 2272 11808

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(4140))\)

We only show spaces with odd 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
4140.3.b \(\chi_{4140}(4139, \cdot)\) n/a 576 1
4140.3.c \(\chi_{4140}(4049, \cdot)\) 4140.3.c.a 88 1
4140.3.d \(\chi_{4140}(2161, \cdot)\) 4140.3.d.a 16 1
4140.3.d.b 32
4140.3.d.c 32
4140.3.e \(\chi_{4140}(2071, \cdot)\) n/a 440 1
4140.3.j \(\chi_{4140}(2899, \cdot)\) n/a 660 1
4140.3.k \(\chi_{4140}(2989, \cdot)\) n/a 120 1
4140.3.l \(\chi_{4140}(3221, \cdot)\) 4140.3.l.a 56 1
4140.3.m \(\chi_{4140}(3311, \cdot)\) n/a 384 1
4140.3.v \(\chi_{4140}(1747, \cdot)\) n/a 1432 2
4140.3.w \(\chi_{4140}(1657, \cdot)\) n/a 220 2
4140.3.x \(\chi_{4140}(323, \cdot)\) n/a 1056 2
4140.3.y \(\chi_{4140}(413, \cdot)\) n/a 192 2
4140.3.bc \(\chi_{4140}(461, \cdot)\) n/a 352 2
4140.3.bd \(\chi_{4140}(551, \cdot)\) n/a 2304 2
4140.3.be \(\chi_{4140}(139, \cdot)\) n/a 3168 2
4140.3.bf \(\chi_{4140}(229, \cdot)\) n/a 576 2
4140.3.bk \(\chi_{4140}(781, \cdot)\) n/a 384 2
4140.3.bl \(\chi_{4140}(691, \cdot)\) n/a 2112 2
4140.3.bm \(\chi_{4140}(1379, \cdot)\) n/a 3440 2
4140.3.bn \(\chi_{4140}(1289, \cdot)\) n/a 528 2
4140.3.bp \(\chi_{4140}(277, \cdot)\) n/a 1056 4
4140.3.bq \(\chi_{4140}(367, \cdot)\) n/a 6880 4
4140.3.br \(\chi_{4140}(137, \cdot)\) n/a 1152 4
4140.3.bs \(\chi_{4140}(47, \cdot)\) n/a 6336 4
4140.3.ca \(\chi_{4140}(251, \cdot)\) n/a 3840 10
4140.3.cb \(\chi_{4140}(1061, \cdot)\) n/a 640 10
4140.3.cc \(\chi_{4140}(109, \cdot)\) n/a 1200 10
4140.3.cd \(\chi_{4140}(739, \cdot)\) n/a 7160 10
4140.3.ci \(\chi_{4140}(271, \cdot)\) n/a 4800 10
4140.3.cj \(\chi_{4140}(181, \cdot)\) n/a 800 10
4140.3.ck \(\chi_{4140}(269, \cdot)\) n/a 960 10
4140.3.cl \(\chi_{4140}(359, \cdot)\) n/a 5760 10
4140.3.cn \(\chi_{4140}(17, \cdot)\) n/a 1920 20
4140.3.co \(\chi_{4140}(647, \cdot)\) n/a 11520 20
4140.3.cp \(\chi_{4140}(73, \cdot)\) n/a 2400 20
4140.3.cq \(\chi_{4140}(343, \cdot)\) n/a 14320 20
4140.3.cv \(\chi_{4140}(29, \cdot)\) n/a 5760 20
4140.3.cw \(\chi_{4140}(419, \cdot)\) n/a 34400 20
4140.3.cx \(\chi_{4140}(31, \cdot)\) n/a 23040 20
4140.3.cy \(\chi_{4140}(61, \cdot)\) n/a 3840 20
4140.3.dd \(\chi_{4140}(589, \cdot)\) n/a 5760 20
4140.3.de \(\chi_{4140}(259, \cdot)\) n/a 34400 20
4140.3.df \(\chi_{4140}(11, \cdot)\) n/a 23040 20
4140.3.dg \(\chi_{4140}(41, \cdot)\) n/a 3840 20
4140.3.do \(\chi_{4140}(167, \cdot)\) n/a 68800 40
4140.3.dp \(\chi_{4140}(113, \cdot)\) n/a 11520 40
4140.3.dq \(\chi_{4140}(7, \cdot)\) n/a 68800 40
4140.3.dr \(\chi_{4140}(13, \cdot)\) n/a 11520 40

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(4140))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(4140)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(828))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1035))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2070))\)\(^{\oplus 2}\)