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Properties

Label 4450.2
Level 4450
Weight 2
Dimension 182442
Nonzero newspaces 32
Sturm bound 2376000

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Defining parameters

Level: \( N \) = \( 4450 = 2 \cdot 5^{2} \cdot 89 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(2376000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4450))\).

Total New Old
Modular forms 598928 182442 416486
Cusp forms 589073 182442 406631
Eisenstein series 9855 0 9855

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4450))\)

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
4450.2.a \(\chi_{4450}(1, \cdot)\) 4450.2.a.a 1 1
4450.2.a.b 1
4450.2.a.c 1
4450.2.a.d 1
4450.2.a.e 1
4450.2.a.f 1
4450.2.a.g 1
4450.2.a.h 1
4450.2.a.i 1
4450.2.a.j 1
4450.2.a.k 1
4450.2.a.l 1
4450.2.a.m 1
4450.2.a.n 1
4450.2.a.o 1
4450.2.a.p 1
4450.2.a.q 2
4450.2.a.r 2
4450.2.a.s 2
4450.2.a.t 2
4450.2.a.u 2
4450.2.a.v 3
4450.2.a.w 3
4450.2.a.x 3
4450.2.a.y 3
4450.2.a.z 3
4450.2.a.ba 3
4450.2.a.bb 3
4450.2.a.bc 3
4450.2.a.bd 5
4450.2.a.be 5
4450.2.a.bf 5
4450.2.a.bg 5
4450.2.a.bh 6
4450.2.a.bi 8
4450.2.a.bj 8
4450.2.a.bk 9
4450.2.a.bl 9
4450.2.a.bm 14
4450.2.a.bn 14
4450.2.b \(\chi_{4450}(2849, \cdot)\) n/a 132 1
4450.2.c \(\chi_{4450}(1601, \cdot)\) n/a 142 1
4450.2.d \(\chi_{4450}(4449, \cdot)\) n/a 136 1
4450.2.f \(\chi_{4450}(301, \cdot)\) n/a 286 2
4450.2.i \(\chi_{4450}(3149, \cdot)\) n/a 268 2
4450.2.k \(\chi_{4450}(891, \cdot)\) n/a 880 4
4450.2.l \(\chi_{4450}(393, \cdot)\) n/a 540 4
4450.2.o \(\chi_{4450}(2593, \cdot)\) n/a 540 4
4450.2.p \(\chi_{4450}(889, \cdot)\) n/a 896 4
4450.2.q \(\chi_{4450}(711, \cdot)\) n/a 904 4
4450.2.r \(\chi_{4450}(179, \cdot)\) n/a 880 4
4450.2.s \(\chi_{4450}(401, \cdot)\) n/a 1420 10
4450.2.u \(\chi_{4450}(479, \cdot)\) n/a 1808 8
4450.2.x \(\chi_{4450}(411, \cdot)\) n/a 1792 8
4450.2.z \(\chi_{4450}(799, \cdot)\) n/a 1360 10
4450.2.ba \(\chi_{4450}(251, \cdot)\) n/a 1420 10
4450.2.bb \(\chi_{4450}(299, \cdot)\) n/a 1360 10
4450.2.bc \(\chi_{4450}(37, \cdot)\) n/a 3600 16
4450.2.bf \(\chi_{4450}(77, \cdot)\) n/a 3600 16
4450.2.bh \(\chi_{4450}(49, \cdot)\) n/a 2680 20
4450.2.bk \(\chi_{4450}(351, \cdot)\) n/a 2860 20
4450.2.bm \(\chi_{4450}(91, \cdot)\) n/a 9040 40
4450.2.bn \(\chi_{4450}(43, \cdot)\) n/a 5400 40
4450.2.bq \(\chi_{4450}(7, \cdot)\) n/a 5400 40
4450.2.br \(\chi_{4450}(39, \cdot)\) n/a 8960 40
4450.2.bs \(\chi_{4450}(11, \cdot)\) n/a 9040 40
4450.2.bt \(\chi_{4450}(139, \cdot)\) n/a 8960 40
4450.2.bv \(\chi_{4450}(21, \cdot)\) n/a 17920 80
4450.2.by \(\chi_{4450}(9, \cdot)\) n/a 18080 80
4450.2.ca \(\chi_{4450}(13, \cdot)\) n/a 36000 160
4450.2.cd \(\chi_{4450}(3, \cdot)\) n/a 36000 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4450))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4450)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(89))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(178))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(445))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(890))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4450))\)\(^{\oplus 1}\)