Properties

Label 448.8
Level 448
Weight 8
Dimension 23074
Nonzero newspaces 16
Sturm bound 98304
Trace bound 25

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Defining parameters

Level: \( N \) = \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(98304\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(448))\).

Total New Old
Modular forms 43440 23294 20146
Cusp forms 42576 23074 19502
Eisenstein series 864 220 644

Trace form

\( 23074 q - 32 q^{2} - 24 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 28 q^{7} - 80 q^{8} + 4334 q^{9} - 32 q^{10} + 2384 q^{11} - 32 q^{12} + 14096 q^{13} - 40 q^{14} - 54064 q^{15} - 32 q^{16} + 11576 q^{17}+ \cdots + 11263484 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(448))\)

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
448.8.a \(\chi_{448}(1, \cdot)\) 448.8.a.a 1 1
448.8.a.b 1
448.8.a.c 1
448.8.a.d 1
448.8.a.e 1
448.8.a.f 1
448.8.a.g 1
448.8.a.h 1
448.8.a.i 1
448.8.a.j 1
448.8.a.k 2
448.8.a.l 2
448.8.a.m 2
448.8.a.n 2
448.8.a.o 2
448.8.a.p 2
448.8.a.q 2
448.8.a.r 2
448.8.a.s 2
448.8.a.t 2
448.8.a.u 3
448.8.a.v 3
448.8.a.w 3
448.8.a.x 3
448.8.a.y 4
448.8.a.z 4
448.8.a.ba 5
448.8.a.bb 5
448.8.a.bc 6
448.8.a.bd 6
448.8.a.be 6
448.8.a.bf 6
448.8.b \(\chi_{448}(225, \cdot)\) 448.8.b.a 14 1
448.8.b.b 14
448.8.b.c 28
448.8.b.d 28
448.8.e \(\chi_{448}(223, \cdot)\) n/a 112 1
448.8.f \(\chi_{448}(447, \cdot)\) n/a 110 1
448.8.i \(\chi_{448}(65, \cdot)\) n/a 220 2
448.8.j \(\chi_{448}(111, \cdot)\) n/a 220 2
448.8.m \(\chi_{448}(113, \cdot)\) n/a 168 2
448.8.p \(\chi_{448}(255, \cdot)\) n/a 220 2
448.8.q \(\chi_{448}(31, \cdot)\) n/a 224 2
448.8.t \(\chi_{448}(289, \cdot)\) n/a 224 2
448.8.u \(\chi_{448}(57, \cdot)\) None 0 4
448.8.x \(\chi_{448}(55, \cdot)\) None 0 4
448.8.z \(\chi_{448}(47, \cdot)\) n/a 440 4
448.8.ba \(\chi_{448}(81, \cdot)\) n/a 440 4
448.8.bc \(\chi_{448}(29, \cdot)\) n/a 2688 8
448.8.bd \(\chi_{448}(27, \cdot)\) n/a 3568 8
448.8.bh \(\chi_{448}(9, \cdot)\) None 0 8
448.8.bi \(\chi_{448}(87, \cdot)\) None 0 8
448.8.bm \(\chi_{448}(3, \cdot)\) n/a 7136 16
448.8.bn \(\chi_{448}(37, \cdot)\) n/a 7136 16

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(448))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(448)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 7}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)