Properties

Label 400.5
Level 400
Weight 5
Dimension 9862
Nonzero newspaces 14
Sturm bound 48000
Trace bound 5

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Defining parameters

Level: \( N \) = \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(48000\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(400))\).

Total New Old
Modular forms 19592 10046 9546
Cusp forms 18808 9862 8946
Eisenstein series 784 184 600

Trace form

\( 9862 q - 26 q^{2} - 20 q^{3} - 32 q^{4} - 40 q^{5} + 24 q^{6} - 22 q^{7} - 116 q^{8} - 232 q^{9} - 32 q^{10} + 64 q^{11} - 356 q^{12} - 156 q^{13} + 20 q^{14} + 648 q^{15} - 208 q^{16} + 650 q^{17} + 1366 q^{18}+ \cdots - 55786 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(400))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
400.5.b \(\chi_{400}(351, \cdot)\) 400.5.b.a 1 1
400.5.b.b 1
400.5.b.c 2
400.5.b.d 2
400.5.b.e 2
400.5.b.f 2
400.5.b.g 4
400.5.b.h 4
400.5.b.i 6
400.5.b.j 6
400.5.b.k 8
400.5.e \(\chi_{400}(199, \cdot)\) None 0 1
400.5.g \(\chi_{400}(151, \cdot)\) None 0 1
400.5.h \(\chi_{400}(399, \cdot)\) 400.5.h.a 4 1
400.5.h.b 4
400.5.h.c 8
400.5.h.d 8
400.5.h.e 12
400.5.i \(\chi_{400}(93, \cdot)\) n/a 284 2
400.5.k \(\chi_{400}(99, \cdot)\) n/a 284 2
400.5.m \(\chi_{400}(57, \cdot)\) None 0 2
400.5.p \(\chi_{400}(193, \cdot)\) 400.5.p.a 2 2
400.5.p.b 2
400.5.p.c 2
400.5.p.d 2
400.5.p.e 4
400.5.p.f 4
400.5.p.g 4
400.5.p.h 4
400.5.p.i 4
400.5.p.j 4
400.5.p.k 4
400.5.p.l 4
400.5.p.m 4
400.5.p.n 4
400.5.p.o 6
400.5.p.p 8
400.5.p.q 8
400.5.r \(\chi_{400}(51, \cdot)\) n/a 298 2
400.5.t \(\chi_{400}(157, \cdot)\) n/a 284 2
400.5.v \(\chi_{400}(71, \cdot)\) None 0 4
400.5.x \(\chi_{400}(79, \cdot)\) n/a 240 4
400.5.z \(\chi_{400}(31, \cdot)\) n/a 240 4
400.5.ba \(\chi_{400}(39, \cdot)\) None 0 4
400.5.bc \(\chi_{400}(53, \cdot)\) n/a 1904 8
400.5.bf \(\chi_{400}(19, \cdot)\) n/a 1904 8
400.5.bg \(\chi_{400}(17, \cdot)\) n/a 472 8
400.5.bj \(\chi_{400}(73, \cdot)\) None 0 8
400.5.bk \(\chi_{400}(11, \cdot)\) n/a 1904 8
400.5.bn \(\chi_{400}(13, \cdot)\) n/a 1904 8

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(400))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(400)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)