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Properties

Label 4140.2
Level 4140
Weight 2
Dimension 191254
Nonzero newspaces 48
Sturm bound 1824768

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Defining parameters

Level: \( N \) = \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(1824768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4140))\).

Total New Old
Modular forms 463232 193518 269714
Cusp forms 449153 191254 257899
Eisenstein series 14079 2264 11815

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4140))\)

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
4140.2.a \(\chi_{4140}(1, \cdot)\) 4140.2.a.a 1 1
4140.2.a.b 1
4140.2.a.c 1
4140.2.a.d 1
4140.2.a.e 1
4140.2.a.f 1
4140.2.a.g 1
4140.2.a.h 1
4140.2.a.i 1
4140.2.a.j 1
4140.2.a.k 1
4140.2.a.l 2
4140.2.a.m 2
4140.2.a.n 2
4140.2.a.o 2
4140.2.a.p 2
4140.2.a.q 2
4140.2.a.r 2
4140.2.a.s 3
4140.2.a.t 5
4140.2.a.u 5
4140.2.f \(\chi_{4140}(829, \cdot)\) 4140.2.f.a 6 1
4140.2.f.b 12
4140.2.f.c 14
4140.2.f.d 24
4140.2.g \(\chi_{4140}(919, \cdot)\) n/a 356 1
4140.2.h \(\chi_{4140}(1151, \cdot)\) n/a 176 1
4140.2.i \(\chi_{4140}(1241, \cdot)\) 4140.2.i.a 16 1
4140.2.i.b 16
4140.2.n \(\chi_{4140}(2069, \cdot)\) 4140.2.n.a 16 1
4140.2.n.b 32
4140.2.o \(\chi_{4140}(1979, \cdot)\) n/a 264 1
4140.2.p \(\chi_{4140}(91, \cdot)\) n/a 240 1
4140.2.q \(\chi_{4140}(1381, \cdot)\) n/a 176 2
4140.2.r \(\chi_{4140}(827, \cdot)\) n/a 576 2
4140.2.s \(\chi_{4140}(737, \cdot)\) 4140.2.s.a 44 2
4140.2.s.b 44
4140.2.t \(\chi_{4140}(1243, \cdot)\) n/a 660 2
4140.2.u \(\chi_{4140}(1333, \cdot)\) n/a 120 2
4140.2.z \(\chi_{4140}(1471, \cdot)\) n/a 1152 2
4140.2.ba \(\chi_{4140}(689, \cdot)\) n/a 288 2
4140.2.bb \(\chi_{4140}(599, \cdot)\) n/a 1584 2
4140.2.bg \(\chi_{4140}(2531, \cdot)\) n/a 1056 2
4140.2.bh \(\chi_{4140}(2621, \cdot)\) n/a 192 2
4140.2.bi \(\chi_{4140}(2209, \cdot)\) n/a 264 2
4140.2.bj \(\chi_{4140}(2299, \cdot)\) n/a 1712 2
4140.2.bo \(\chi_{4140}(361, \cdot)\) n/a 400 10
4140.2.bt \(\chi_{4140}(1013, \cdot)\) n/a 528 4
4140.2.bu \(\chi_{4140}(1103, \cdot)\) n/a 3424 4
4140.2.bv \(\chi_{4140}(1057, \cdot)\) n/a 576 4
4140.2.bw \(\chi_{4140}(967, \cdot)\) n/a 3168 4
4140.2.bx \(\chi_{4140}(451, \cdot)\) n/a 2400 10
4140.2.by \(\chi_{4140}(179, \cdot)\) n/a 2880 10
4140.2.bz \(\chi_{4140}(89, \cdot)\) n/a 480 10
4140.2.ce \(\chi_{4140}(341, \cdot)\) n/a 320 10
4140.2.cf \(\chi_{4140}(71, \cdot)\) n/a 1920 10
4140.2.cg \(\chi_{4140}(19, \cdot)\) n/a 3560 10
4140.2.ch \(\chi_{4140}(289, \cdot)\) n/a 600 10
4140.2.cm \(\chi_{4140}(121, \cdot)\) n/a 1920 20
4140.2.cr \(\chi_{4140}(37, \cdot)\) n/a 1200 20
4140.2.cs \(\chi_{4140}(127, \cdot)\) n/a 7120 20
4140.2.ct \(\chi_{4140}(197, \cdot)\) n/a 960 20
4140.2.cu \(\chi_{4140}(107, \cdot)\) n/a 5760 20
4140.2.cz \(\chi_{4140}(79, \cdot)\) n/a 17120 20
4140.2.da \(\chi_{4140}(49, \cdot)\) n/a 2880 20
4140.2.db \(\chi_{4140}(221, \cdot)\) n/a 1920 20
4140.2.dc \(\chi_{4140}(131, \cdot)\) n/a 11520 20
4140.2.dh \(\chi_{4140}(59, \cdot)\) n/a 17120 20
4140.2.di \(\chi_{4140}(149, \cdot)\) n/a 2880 20
4140.2.dj \(\chi_{4140}(511, \cdot)\) n/a 11520 20
4140.2.dk \(\chi_{4140}(187, \cdot)\) n/a 34240 40
4140.2.dl \(\chi_{4140}(97, \cdot)\) n/a 5760 40
4140.2.dm \(\chi_{4140}(83, \cdot)\) n/a 34240 40
4140.2.dn \(\chi_{4140}(77, \cdot)\) n/a 5760 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4140))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4140)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(828))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1035))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2070))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4140))\)\(^{\oplus 1}\)