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Properties

Label 2432.1
Level 2432
Weight 1
Dimension 54
Nonzero newspaces 6
Newform subspaces 16
Sturm bound 368640
Trace bound 9

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Defining parameters

Level: \( N \) = \( 2432 = 2^{7} \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 16 \)
Sturm bound: \(368640\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2432))\).

Total New Old
Modular forms 3094 870 2224
Cusp forms 214 54 160
Eisenstein series 2880 816 2064

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 38 0 16 0

Trace form

\( 54 q - 6 q^{9} + O(q^{10}) \) \( 54 q - 6 q^{9} + 16 q^{17} + 6 q^{25} + 4 q^{33} - 8 q^{41} - 2 q^{49} - 4 q^{57} - 4 q^{73} - 10 q^{81} + 4 q^{89} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2432))\)

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
2432.1.d \(\chi_{2432}(1407, \cdot)\) None 0 1
2432.1.e \(\chi_{2432}(1025, \cdot)\) 2432.1.e.a 2 1
2432.1.e.b 2
2432.1.e.c 2
2432.1.e.d 2
2432.1.f \(\chi_{2432}(191, \cdot)\) None 0 1
2432.1.g \(\chi_{2432}(2241, \cdot)\) 2432.1.g.a 1 1
2432.1.g.b 1
2432.1.g.c 2
2432.1.g.d 2
2432.1.j \(\chi_{2432}(417, \cdot)\) None 0 2
2432.1.l \(\chi_{2432}(799, \cdot)\) None 0 2
2432.1.o \(\chi_{2432}(1983, \cdot)\) 2432.1.o.a 4 2
2432.1.o.b 4
2432.1.o.c 4
2432.1.p \(\chi_{2432}(65, \cdot)\) 2432.1.p.a 2 2
2432.1.p.b 2
2432.1.q \(\chi_{2432}(767, \cdot)\) None 0 2
2432.1.r \(\chi_{2432}(1281, \cdot)\) None 0 2
2432.1.w \(\chi_{2432}(113, \cdot)\) None 0 4
2432.1.x \(\chi_{2432}(495, \cdot)\) None 0 4
2432.1.ba \(\chi_{2432}(673, \cdot)\) None 0 4
2432.1.bc \(\chi_{2432}(159, \cdot)\) None 0 4
2432.1.bf \(\chi_{2432}(39, \cdot)\) None 0 8
2432.1.bg \(\chi_{2432}(265, \cdot)\) None 0 8
2432.1.bh \(\chi_{2432}(129, \cdot)\) None 0 6
2432.1.bi \(\chi_{2432}(193, \cdot)\) 2432.1.bi.a 6 6
2432.1.bi.b 6
2432.1.bk \(\chi_{2432}(63, \cdot)\) 2432.1.bk.a 12 6
2432.1.bn \(\chi_{2432}(511, \cdot)\) None 0 6
2432.1.bo \(\chi_{2432}(239, \cdot)\) None 0 8
2432.1.bp \(\chi_{2432}(145, \cdot)\) None 0 8
2432.1.bt \(\chi_{2432}(37, \cdot)\) None 0 16
2432.1.bu \(\chi_{2432}(115, \cdot)\) None 0 16
2432.1.bx \(\chi_{2432}(351, \cdot)\) None 0 12
2432.1.bz \(\chi_{2432}(33, \cdot)\) None 0 12
2432.1.cc \(\chi_{2432}(217, \cdot)\) None 0 16
2432.1.cd \(\chi_{2432}(7, \cdot)\) None 0 16
2432.1.cg \(\chi_{2432}(47, \cdot)\) None 0 24
2432.1.ch \(\chi_{2432}(241, \cdot)\) None 0 24
2432.1.ci \(\chi_{2432}(11, \cdot)\) None 0 32
2432.1.cl \(\chi_{2432}(69, \cdot)\) None 0 32
2432.1.cm \(\chi_{2432}(23, \cdot)\) None 0 48
2432.1.cn \(\chi_{2432}(41, \cdot)\) None 0 48
2432.1.cq \(\chi_{2432}(13, \cdot)\) None 0 96
2432.1.ct \(\chi_{2432}(35, \cdot)\) None 0 96

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2432))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2432)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1216))\)\(^{\oplus 2}\)