↑

Properties

Label 2416.1
Level 2416
Weight 1
Dimension 25
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 364800
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2416 = 2^{4} \cdot 151 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(364800\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2416))\).

Total New Old
Modular forms 2162 696 1466
Cusp forms 62 25 37
Eisenstein series 2100 671 1429

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 17 0 0 8

Trace form

\( 25 q - q^{5} + 3 q^{9} + q^{11} - 2 q^{13} + q^{17} + q^{19} - 2 q^{21} + 6 q^{25} + 3 q^{29} + q^{31} + 2 q^{33} + q^{37} - 14 q^{38} - 4 q^{41} + q^{43} - 14 q^{44} - q^{45} + q^{47} - 9 q^{49}+ \cdots + q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2416))\)

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
2416.1.d \(\chi_{2416}(303, \cdot)\) None 0 1
2416.1.e \(\chi_{2416}(2113, \cdot)\) 2416.1.e.a 3 1
2416.1.f \(\chi_{2416}(905, \cdot)\) None 0 1
2416.1.g \(\chi_{2416}(1511, \cdot)\) None 0 1
2416.1.l \(\chi_{2416}(907, \cdot)\) None 0 2
2416.1.m \(\chi_{2416}(301, \cdot)\) 2416.1.m.a 2 2
2416.1.m.b 12
2416.1.o \(\chi_{2416}(33, \cdot)\) None 0 2
2416.1.p \(\chi_{2416}(1391, \cdot)\) 2416.1.p.a 8 2
2416.1.t \(\chi_{2416}(183, \cdot)\) None 0 2
2416.1.u \(\chi_{2416}(1241, \cdot)\) None 0 2
2416.1.w \(\chi_{2416}(215, \cdot)\) None 0 4
2416.1.x \(\chi_{2416}(585, \cdot)\) None 0 4
2416.1.y \(\chi_{2416}(545, \cdot)\) None 0 4
2416.1.z \(\chi_{2416}(159, \cdot)\) None 0 4
2416.1.bc \(\chi_{2416}(421, \cdot)\) None 0 4
2416.1.bd \(\chi_{2416}(571, \cdot)\) None 0 4
2416.1.bh \(\chi_{2416}(389, \cdot)\) None 0 8
2416.1.bi \(\chi_{2416}(19, \cdot)\) None 0 8
2416.1.bm \(\chi_{2416}(217, \cdot)\) None 0 8
2416.1.bn \(\chi_{2416}(167, \cdot)\) None 0 8
2416.1.br \(\chi_{2416}(831, \cdot)\) None 0 8
2416.1.bs \(\chi_{2416}(113, \cdot)\) None 0 8
2416.1.bu \(\chi_{2416}(65, \cdot)\) None 0 20
2416.1.bv \(\chi_{2416}(311, \cdot)\) None 0 20
2416.1.by \(\chi_{2416}(41, \cdot)\) None 0 20
2416.1.bz \(\chi_{2416}(127, \cdot)\) None 0 20
2416.1.cc \(\chi_{2416}(155, \cdot)\) None 0 16
2416.1.cd \(\chi_{2416}(149, \cdot)\) None 0 16
2416.1.cf \(\chi_{2416}(53, \cdot)\) None 0 40
2416.1.cg \(\chi_{2416}(91, \cdot)\) None 0 40
2416.1.cj \(\chi_{2416}(39, \cdot)\) None 0 40
2416.1.ck \(\chi_{2416}(129, \cdot)\) None 0 40
2416.1.cm \(\chi_{2416}(31, \cdot)\) None 0 40
2416.1.cn \(\chi_{2416}(89, \cdot)\) None 0 40
2416.1.cs \(\chi_{2416}(11, \cdot)\) None 0 80
2416.1.ct \(\chi_{2416}(13, \cdot)\) None 0 80

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2416))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2416)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(302))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(604))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1208))\)\(^{\oplus 2}\)