Properties

Label 4025.2
Level 4025
Weight 2
Dimension 553208
Nonzero newspaces 48
Sturm bound 2534400

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Defining parameters

Level: \( N \) = \( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(2534400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4025))\).

Total New Old
Modular forms 640992 561820 79172
Cusp forms 626209 553208 73001
Eisenstein series 14783 8612 6171

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4025))\)

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
4025.2.a \(\chi_{4025}(1, \cdot)\) 4025.2.a.a 1 1
4025.2.a.b 1
4025.2.a.c 1
4025.2.a.d 1
4025.2.a.e 1
4025.2.a.f 1
4025.2.a.g 1
4025.2.a.h 2
4025.2.a.i 2
4025.2.a.j 3
4025.2.a.k 3
4025.2.a.l 4
4025.2.a.m 4
4025.2.a.n 4
4025.2.a.o 4
4025.2.a.p 5
4025.2.a.q 5
4025.2.a.r 5
4025.2.a.s 8
4025.2.a.t 8
4025.2.a.u 8
4025.2.a.v 8
4025.2.a.w 8
4025.2.a.x 12
4025.2.a.y 12
4025.2.a.z 14
4025.2.a.ba 14
4025.2.a.bb 14
4025.2.a.bc 14
4025.2.a.bd 21
4025.2.a.be 21
4025.2.c \(\chi_{4025}(2899, \cdot)\) n/a 196 1
4025.2.d \(\chi_{4025}(4024, \cdot)\) n/a 284 1
4025.2.f \(\chi_{4025}(1126, \cdot)\) n/a 298 1
4025.2.i \(\chi_{4025}(576, \cdot)\) n/a 556 2
4025.2.k \(\chi_{4025}(2232, \cdot)\) n/a 528 2
4025.2.l \(\chi_{4025}(1632, \cdot)\) n/a 432 2
4025.2.n \(\chi_{4025}(806, \cdot)\) n/a 1312 4
4025.2.q \(\chi_{4025}(551, \cdot)\) n/a 596 2
4025.2.s \(\chi_{4025}(2299, \cdot)\) n/a 568 2
4025.2.t \(\chi_{4025}(599, \cdot)\) n/a 528 2
4025.2.x \(\chi_{4025}(321, \cdot)\) n/a 1904 4
4025.2.z \(\chi_{4025}(804, \cdot)\) n/a 1904 4
4025.2.ba \(\chi_{4025}(484, \cdot)\) n/a 1328 4
4025.2.bc \(\chi_{4025}(351, \cdot)\) n/a 2280 10
4025.2.bd \(\chi_{4025}(507, \cdot)\) n/a 1056 4
4025.2.bg \(\chi_{4025}(2207, \cdot)\) n/a 1136 4
4025.2.bh \(\chi_{4025}(116, \cdot)\) n/a 3520 8
4025.2.bj \(\chi_{4025}(22, \cdot)\) n/a 2880 8
4025.2.bk \(\chi_{4025}(622, \cdot)\) n/a 3520 8
4025.2.bo \(\chi_{4025}(76, \cdot)\) n/a 2980 10
4025.2.bq \(\chi_{4025}(1049, \cdot)\) n/a 2840 10
4025.2.br \(\chi_{4025}(449, \cdot)\) n/a 2160 10
4025.2.bu \(\chi_{4025}(254, \cdot)\) n/a 3520 8
4025.2.bv \(\chi_{4025}(229, \cdot)\) n/a 3808 8
4025.2.bx \(\chi_{4025}(206, \cdot)\) n/a 3808 8
4025.2.ca \(\chi_{4025}(151, \cdot)\) n/a 5960 20
4025.2.cc \(\chi_{4025}(43, \cdot)\) n/a 4320 20
4025.2.cd \(\chi_{4025}(118, \cdot)\) n/a 5680 20
4025.2.cf \(\chi_{4025}(36, \cdot)\) n/a 14400 40
4025.2.cg \(\chi_{4025}(137, \cdot)\) n/a 7616 16
4025.2.cj \(\chi_{4025}(47, \cdot)\) n/a 7040 16
4025.2.cl \(\chi_{4025}(324, \cdot)\) n/a 5680 20
4025.2.cm \(\chi_{4025}(199, \cdot)\) n/a 5680 20
4025.2.co \(\chi_{4025}(201, \cdot)\) n/a 5960 20
4025.2.cs \(\chi_{4025}(29, \cdot)\) n/a 14400 40
4025.2.ct \(\chi_{4025}(34, \cdot)\) n/a 19040 40
4025.2.cv \(\chi_{4025}(111, \cdot)\) n/a 19040 40
4025.2.cy \(\chi_{4025}(107, \cdot)\) n/a 11360 40
4025.2.db \(\chi_{4025}(82, \cdot)\) n/a 11360 40
4025.2.dc \(\chi_{4025}(16, \cdot)\) n/a 38080 80
4025.2.de \(\chi_{4025}(13, \cdot)\) n/a 38080 80
4025.2.df \(\chi_{4025}(113, \cdot)\) n/a 28800 80
4025.2.dj \(\chi_{4025}(61, \cdot)\) n/a 38080 80
4025.2.dl \(\chi_{4025}(19, \cdot)\) n/a 38080 80
4025.2.dm \(\chi_{4025}(4, \cdot)\) n/a 38080 80
4025.2.do \(\chi_{4025}(3, \cdot)\) n/a 76160 160
4025.2.dr \(\chi_{4025}(37, \cdot)\) n/a 76160 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4025)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(575))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(805))\)\(^{\oplus 2}\)