Properties

Label 2944.1
Level 2944
Weight 1
Dimension 76
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 540672
Trace bound 27

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2944 = 2^{7} \cdot 23 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(540672\)
Trace bound: \(27\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2944))\).

Total New Old
Modular forms 3758 1084 2674
Cusp forms 238 76 162
Eisenstein series 3520 1008 2512

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 76 0 0 0

Trace form

\( 76 q + 4 q^{9} + 4 q^{25} + 12 q^{27} + 12 q^{39} - 8 q^{49} - 48 q^{58} - 48 q^{72} - 8 q^{81} + 12 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2944))\)

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
2944.1.d \(\chi_{2944}(1151, \cdot)\) None 0 1
2944.1.e \(\chi_{2944}(321, \cdot)\) 2944.1.e.a 2 1
2944.1.e.b 2
2944.1.f \(\chi_{2944}(1793, \cdot)\) None 0 1
2944.1.g \(\chi_{2944}(2623, \cdot)\) None 0 1
2944.1.k \(\chi_{2944}(1057, \cdot)\) 2944.1.k.a 2 2
2944.1.k.b 2
2944.1.k.c 4
2944.1.k.d 4
2944.1.l \(\chi_{2944}(415, \cdot)\) None 0 2
2944.1.o \(\chi_{2944}(47, \cdot)\) None 0 4
2944.1.p \(\chi_{2944}(689, \cdot)\) 2944.1.p.a 4 4
2944.1.p.b 8
2944.1.s \(\chi_{2944}(137, \cdot)\) None 0 8
2944.1.t \(\chi_{2944}(231, \cdot)\) None 0 8
2944.1.w \(\chi_{2944}(703, \cdot)\) None 0 10
2944.1.x \(\chi_{2944}(129, \cdot)\) None 0 10
2944.1.y \(\chi_{2944}(65, \cdot)\) None 0 10
2944.1.z \(\chi_{2944}(127, \cdot)\) None 0 10
2944.1.be \(\chi_{2944}(139, \cdot)\) None 0 16
2944.1.bf \(\chi_{2944}(45, \cdot)\) 2944.1.bf.a 16 16
2944.1.bf.b 32
2944.1.bg \(\chi_{2944}(31, \cdot)\) None 0 20
2944.1.bh \(\chi_{2944}(33, \cdot)\) None 0 20
2944.1.bk \(\chi_{2944}(17, \cdot)\) None 0 40
2944.1.bl \(\chi_{2944}(239, \cdot)\) None 0 40
2944.1.bp \(\chi_{2944}(39, \cdot)\) None 0 80
2944.1.bq \(\chi_{2944}(57, \cdot)\) None 0 80
2944.1.bs \(\chi_{2944}(5, \cdot)\) None 0 160
2944.1.bt \(\chi_{2944}(3, \cdot)\) None 0 160

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2944))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2944)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 14}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(736))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1472))\)\(^{\oplus 2}\)