Properties

Label 320.5
Level 320
Weight 5
Dimension 6270
Nonzero newspaces 14
Sturm bound 30720
Trace bound 12

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Defining parameters

Level: \( N \) = \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(30720\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(320))\).

Total New Old
Modular forms 12576 6402 6174
Cusp forms 12000 6270 5730
Eisenstein series 576 132 444

Trace form

\( 6270 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 24 q^{5} - 48 q^{6} - 16 q^{7} - 16 q^{8} - 182 q^{9} - 24 q^{10} + 156 q^{11} - 16 q^{12} + 688 q^{13} - 16 q^{14} - 16 q^{15} - 48 q^{16} - 988 q^{17} - 16 q^{18}+ \cdots + 44636 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(320))\)

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
320.5.b \(\chi_{320}(191, \cdot)\) 320.5.b.a 4 1
320.5.b.b 4
320.5.b.c 8
320.5.b.d 8
320.5.b.e 8
320.5.e \(\chi_{320}(159, \cdot)\) 320.5.e.a 16 1
320.5.e.b 32
320.5.g \(\chi_{320}(31, \cdot)\) 320.5.g.a 8 1
320.5.g.b 24
320.5.h \(\chi_{320}(319, \cdot)\) 320.5.h.a 1 1
320.5.h.b 1
320.5.h.c 2
320.5.h.d 2
320.5.h.e 8
320.5.h.f 8
320.5.h.g 12
320.5.h.h 12
320.5.i \(\chi_{320}(177, \cdot)\) 320.5.i.a 92 2
320.5.k \(\chi_{320}(79, \cdot)\) 320.5.k.a 92 2
320.5.m \(\chi_{320}(33, \cdot)\) 320.5.m.a 16 2
320.5.m.b 16
320.5.m.c 32
320.5.m.d 32
320.5.p \(\chi_{320}(193, \cdot)\) 320.5.p.a 2 2
320.5.p.b 2
320.5.p.c 2
320.5.p.d 2
320.5.p.e 2
320.5.p.f 2
320.5.p.g 2
320.5.p.h 2
320.5.p.i 2
320.5.p.j 2
320.5.p.k 4
320.5.p.l 4
320.5.p.m 4
320.5.p.n 4
320.5.p.o 6
320.5.p.p 6
320.5.p.q 8
320.5.p.r 12
320.5.p.s 12
320.5.p.t 12
320.5.r \(\chi_{320}(111, \cdot)\) 320.5.r.a 64 2
320.5.t \(\chi_{320}(17, \cdot)\) 320.5.t.a 92 2
320.5.v \(\chi_{320}(57, \cdot)\) None 0 4
320.5.w \(\chi_{320}(71, \cdot)\) None 0 4
320.5.y \(\chi_{320}(39, \cdot)\) None 0 4
320.5.bb \(\chi_{320}(137, \cdot)\) None 0 4
320.5.bc \(\chi_{320}(53, \cdot)\) n/a 1520 8
320.5.bg \(\chi_{320}(11, \cdot)\) n/a 1024 8
320.5.bh \(\chi_{320}(19, \cdot)\) n/a 1520 8
320.5.bi \(\chi_{320}(13, \cdot)\) n/a 1520 8

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(320))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(320)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 7}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)