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Properties

Label 4225.2
Level 4225
Weight 2
Dimension 642287
Nonzero newspaces 48
Sturm bound 2839200

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Defining parameters

Level: \( N \) = \( 4225 = 5^{2} \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(2839200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4225))\).

Total New Old
Modular forms 716184 650672 65512
Cusp forms 703417 642287 61130
Eisenstein series 12767 8385 4382

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4225))\)

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
4225.2.a \(\chi_{4225}(1, \cdot)\) 4225.2.a.a 1 1
4225.2.a.b 1
4225.2.a.c 1
4225.2.a.d 1
4225.2.a.e 1
4225.2.a.f 1
4225.2.a.g 1
4225.2.a.h 1
4225.2.a.i 1
4225.2.a.j 1
4225.2.a.k 1
4225.2.a.l 1
4225.2.a.m 1
4225.2.a.n 1
4225.2.a.o 1
4225.2.a.p 1
4225.2.a.q 1
4225.2.a.r 2
4225.2.a.s 2
4225.2.a.t 2
4225.2.a.u 2
4225.2.a.v 2
4225.2.a.w 2
4225.2.a.x 2
4225.2.a.y 2
4225.2.a.z 2
4225.2.a.ba 3
4225.2.a.bb 3
4225.2.a.bc 3
4225.2.a.bd 3
4225.2.a.be 3
4225.2.a.bf 3
4225.2.a.bg 3
4225.2.a.bh 3
4225.2.a.bi 4
4225.2.a.bj 4
4225.2.a.bk 4
4225.2.a.bl 4
4225.2.a.bm 5
4225.2.a.bn 5
4225.2.a.bo 5
4225.2.a.bp 5
4225.2.a.bq 6
4225.2.a.br 6
4225.2.a.bs 9
4225.2.a.bt 9
4225.2.a.bu 10
4225.2.a.bv 10
4225.2.a.bw 12
4225.2.a.bx 12
4225.2.a.by 12
4225.2.a.bz 12
4225.2.a.ca 18
4225.2.a.cb 18
4225.2.b \(\chi_{4225}(2874, \cdot)\) n/a 222 1
4225.2.c \(\chi_{4225}(1351, \cdot)\) n/a 230 1
4225.2.d \(\chi_{4225}(4224, \cdot)\) n/a 220 1
4225.2.e \(\chi_{4225}(2726, \cdot)\) n/a 456 2
4225.2.f \(\chi_{4225}(1282, \cdot)\) n/a 442 2
4225.2.k \(\chi_{4225}(268, \cdot)\) n/a 442 2
4225.2.l \(\chi_{4225}(846, \cdot)\) n/a 1508 4
4225.2.m \(\chi_{4225}(699, \cdot)\) n/a 440 2
4225.2.n \(\chi_{4225}(2051, \cdot)\) n/a 458 2
4225.2.o \(\chi_{4225}(1374, \cdot)\) n/a 444 2
4225.2.p \(\chi_{4225}(844, \cdot)\) n/a 1504 4
4225.2.q \(\chi_{4225}(506, \cdot)\) n/a 1496 4
4225.2.r \(\chi_{4225}(339, \cdot)\) n/a 1504 4
4225.2.s \(\chi_{4225}(357, \cdot)\) n/a 884 4
4225.2.x \(\chi_{4225}(418, \cdot)\) n/a 884 4
4225.2.y \(\chi_{4225}(326, \cdot)\) n/a 3420 12
4225.2.z \(\chi_{4225}(146, \cdot)\) n/a 3008 8
4225.2.ba \(\chi_{4225}(577, \cdot)\) n/a 3000 8
4225.2.bf \(\chi_{4225}(408, \cdot)\) n/a 3000 8
4225.2.bg \(\chi_{4225}(324, \cdot)\) n/a 3264 12
4225.2.bh \(\chi_{4225}(51, \cdot)\) n/a 3408 12
4225.2.bi \(\chi_{4225}(274, \cdot)\) n/a 3240 12
4225.2.bj \(\chi_{4225}(484, \cdot)\) n/a 2992 8
4225.2.bk \(\chi_{4225}(316, \cdot)\) n/a 2992 8
4225.2.bl \(\chi_{4225}(654, \cdot)\) n/a 3008 8
4225.2.bm \(\chi_{4225}(126, \cdot)\) n/a 6864 24
4225.2.bn \(\chi_{4225}(57, \cdot)\) n/a 6504 24
4225.2.bs \(\chi_{4225}(18, \cdot)\) n/a 6504 24
4225.2.bt \(\chi_{4225}(188, \cdot)\) n/a 6000 16
4225.2.by \(\chi_{4225}(258, \cdot)\) n/a 6000 16
4225.2.bz \(\chi_{4225}(66, \cdot)\) n/a 21696 48
4225.2.ca \(\chi_{4225}(74, \cdot)\) n/a 6480 24
4225.2.cb \(\chi_{4225}(101, \cdot)\) n/a 6840 24
4225.2.cc \(\chi_{4225}(49, \cdot)\) n/a 6528 24
4225.2.cd \(\chi_{4225}(14, \cdot)\) n/a 21792 48
4225.2.ce \(\chi_{4225}(116, \cdot)\) n/a 21792 48
4225.2.cf \(\chi_{4225}(64, \cdot)\) n/a 21696 48
4225.2.cg \(\chi_{4225}(7, \cdot)\) n/a 13008 48
4225.2.cl \(\chi_{4225}(32, \cdot)\) n/a 13008 48
4225.2.cm \(\chi_{4225}(16, \cdot)\) n/a 43392 96
4225.2.cn \(\chi_{4225}(47, \cdot)\) n/a 43488 96
4225.2.cs \(\chi_{4225}(8, \cdot)\) n/a 43488 96
4225.2.ct \(\chi_{4225}(4, \cdot)\) n/a 43392 96
4225.2.cu \(\chi_{4225}(36, \cdot)\) n/a 43584 96
4225.2.cv \(\chi_{4225}(9, \cdot)\) n/a 43584 96
4225.2.cw \(\chi_{4225}(2, \cdot)\) n/a 86976 192
4225.2.db \(\chi_{4225}(28, \cdot)\) n/a 86976 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4225))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4225)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 2}\)