↑

Properties

Label 456.1
Level 456
Weight 1
Dimension 18
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 11520
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(11520\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(456))\).

Total New Old
Modular forms 494 86 408
Cusp forms 62 18 44
Eisenstein series 432 68 364

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 18 0 0 0

Trace form

\( 18 q - 18 q^{22} - 9 q^{27} + 9 q^{48} - 9 q^{51} + 9 q^{72} - 18 q^{73} + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(456))\)

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
456.1.b \(\chi_{456}(455, \cdot)\) None 0 1
456.1.c \(\chi_{456}(115, \cdot)\) None 0 1
456.1.h \(\chi_{456}(305, \cdot)\) None 0 1
456.1.i \(\chi_{456}(37, \cdot)\) None 0 1
456.1.l \(\chi_{456}(227, \cdot)\) 456.1.l.a 1 1
456.1.l.b 1
456.1.m \(\chi_{456}(343, \cdot)\) None 0 1
456.1.n \(\chi_{456}(77, \cdot)\) None 0 1
456.1.o \(\chi_{456}(265, \cdot)\) None 0 1
456.1.r \(\chi_{456}(7, \cdot)\) None 0 2
456.1.s \(\chi_{456}(107, \cdot)\) 456.1.s.a 2 2
456.1.s.b 2
456.1.w \(\chi_{456}(145, \cdot)\) None 0 2
456.1.x \(\chi_{456}(125, \cdot)\) None 0 2
456.1.ba \(\chi_{456}(163, \cdot)\) None 0 2
456.1.bb \(\chi_{456}(335, \cdot)\) None 0 2
456.1.bc \(\chi_{456}(373, \cdot)\) None 0 2
456.1.bd \(\chi_{456}(353, \cdot)\) None 0 2
456.1.bh \(\chi_{456}(5, \cdot)\) None 0 6
456.1.bi \(\chi_{456}(97, \cdot)\) None 0 6
456.1.bl \(\chi_{456}(17, \cdot)\) None 0 6
456.1.bn \(\chi_{456}(13, \cdot)\) None 0 6
456.1.bo \(\chi_{456}(71, \cdot)\) None 0 6
456.1.bq \(\chi_{456}(43, \cdot)\) None 0 6
456.1.bt \(\chi_{456}(59, \cdot)\) 456.1.bt.a 6 6
456.1.bt.b 6
456.1.bv \(\chi_{456}(55, \cdot)\) None 0 6

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(456))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(456)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 1}\)