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Properties

Label 2420.1
Level 2420
Weight 1
Dimension 168
Nonzero newspaces 7
Newform subspaces 27
Sturm bound 348480
Trace bound 3

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Defining parameters

Level: \( N \) = \( 2420 = 2^{2} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 27 \)
Sturm bound: \(348480\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2420))\).

Total New Old
Modular forms 3452 1010 2442
Cusp forms 252 168 84
Eisenstein series 3200 842 2358

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 168 0 0 0

Trace form

\( 168 q - q^{5} + 4 q^{9} - 3 q^{15} + 10 q^{23} + q^{25} - 2 q^{31} - 48 q^{45} + 2 q^{49} - 20 q^{56} + 2 q^{59} - 10 q^{67} - 6 q^{69} + 2 q^{71} - 3 q^{75} - 2 q^{81} - 12 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2420))\)

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
2420.1.c \(\chi_{2420}(1211, \cdot)\) None 0 1
2420.1.e \(\chi_{2420}(1209, \cdot)\) None 0 1
2420.1.f \(\chi_{2420}(241, \cdot)\) None 0 1
2420.1.h \(\chi_{2420}(2179, \cdot)\) 2420.1.h.a 1 1
2420.1.h.b 1
2420.1.h.c 1
2420.1.h.d 1
2420.1.h.e 1
2420.1.h.f 1
2420.1.h.g 2
2420.1.h.h 2
2420.1.h.i 2
2420.1.h.j 4
2420.1.i \(\chi_{2420}(483, \cdot)\) 2420.1.i.a 4 2
2420.1.i.b 8
2420.1.j \(\chi_{2420}(1453, \cdot)\) 2420.1.j.a 4 2
2420.1.n \(\chi_{2420}(1219, \cdot)\) 2420.1.n.a 4 4
2420.1.n.b 4
2420.1.n.c 4
2420.1.n.d 4
2420.1.n.e 4
2420.1.n.f 4
2420.1.n.g 8
2420.1.n.h 8
2420.1.n.i 8
2420.1.n.j 16
2420.1.p \(\chi_{2420}(161, \cdot)\) None 0 4
2420.1.q \(\chi_{2420}(1129, \cdot)\) 2420.1.q.a 8 4
2420.1.s \(\chi_{2420}(251, \cdot)\) None 0 4
2420.1.x \(\chi_{2420}(403, \cdot)\) 2420.1.x.a 16 8
2420.1.x.b 32
2420.1.y \(\chi_{2420}(493, \cdot)\) 2420.1.y.a 16 8
2420.1.z \(\chi_{2420}(109, \cdot)\) None 0 10
2420.1.bb \(\chi_{2420}(111, \cdot)\) None 0 10
2420.1.bd \(\chi_{2420}(199, \cdot)\) None 0 10
2420.1.bf \(\chi_{2420}(21, \cdot)\) None 0 10
2420.1.bi \(\chi_{2420}(133, \cdot)\) None 0 20
2420.1.bj \(\chi_{2420}(43, \cdot)\) None 0 20
2420.1.bl \(\chi_{2420}(41, \cdot)\) None 0 40
2420.1.bn \(\chi_{2420}(59, \cdot)\) None 0 40
2420.1.bp \(\chi_{2420}(31, \cdot)\) None 0 40
2420.1.br \(\chi_{2420}(29, \cdot)\) None 0 40
2420.1.bs \(\chi_{2420}(37, \cdot)\) None 0 80
2420.1.bt \(\chi_{2420}(7, \cdot)\) None 0 80

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2420))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2420)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1210))\)\(^{\oplus 2}\)