Properties

Label 290.2
Level 290
Weight 2
Dimension 771
Nonzero newspaces 12
Newform subspaces 37
Sturm bound 10080
Trace bound 4

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Defining parameters

Level: \( N \) = \( 290 = 2 \cdot 5 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 37 \)
Sturm bound: \(10080\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(290))\).

Total New Old
Modular forms 2744 771 1973
Cusp forms 2297 771 1526
Eisenstein series 447 0 447

Trace form

\( 771 q + q^{2} + 4 q^{3} + q^{4} + q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + q^{10} + 12 q^{11} + 4 q^{12} + 14 q^{13} + 8 q^{14} + 4 q^{15} + q^{16} + 18 q^{17} + 13 q^{18} + 20 q^{19} - 6 q^{20}+ \cdots - 236 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)

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
290.2.a \(\chi_{290}(1, \cdot)\) 290.2.a.a 1 1
290.2.a.b 2
290.2.a.c 2
290.2.a.d 3
290.2.a.e 3
290.2.b \(\chi_{290}(59, \cdot)\) 290.2.b.a 4 1
290.2.b.b 10
290.2.c \(\chi_{290}(231, \cdot)\) 290.2.c.a 2 1
290.2.c.b 4
290.2.c.c 4
290.2.d \(\chi_{290}(289, \cdot)\) 290.2.d.a 8 1
290.2.d.b 8
290.2.e \(\chi_{290}(17, \cdot)\) 290.2.e.a 2 2
290.2.e.b 2
290.2.e.c 2
290.2.e.d 4
290.2.e.e 8
290.2.e.f 12
290.2.j \(\chi_{290}(133, \cdot)\) 290.2.j.a 2 2
290.2.j.b 2
290.2.j.c 2
290.2.j.d 4
290.2.j.e 8
290.2.j.f 12
290.2.k \(\chi_{290}(81, \cdot)\) 290.2.k.a 12 6
290.2.k.b 12
290.2.k.c 18
290.2.k.d 18
290.2.l \(\chi_{290}(9, \cdot)\) 290.2.l.a 48 6
290.2.l.b 48
290.2.m \(\chi_{290}(51, \cdot)\) 290.2.m.a 24 6
290.2.m.b 36
290.2.n \(\chi_{290}(49, \cdot)\) 290.2.n.a 84 6
290.2.o \(\chi_{290}(3, \cdot)\) 290.2.o.a 84 12
290.2.o.b 96
290.2.t \(\chi_{290}(73, \cdot)\) 290.2.t.a 84 12
290.2.t.b 96

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(290))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(290)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 2}\)