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Properties

Label 2888.1
Level 2888
Weight 1
Dimension 242
Nonzero newspaces 8
Newform subspaces 21
Sturm bound 519840
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2888 = 2^{3} \cdot 19^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 21 \)
Sturm bound: \(519840\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2888))\).

Total New Old
Modular forms 3414 1179 2235
Cusp forms 390 242 148
Eisenstein series 3024 937 2087

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 242 0 0 0

Trace form

\( 242 q + q^{2} + 2 q^{3} - q^{4} + 4 q^{6} + 2 q^{7} + q^{8} + 3 q^{9} + O(q^{10}) \) \( 242 q + q^{2} + 2 q^{3} - q^{4} + 4 q^{6} + 2 q^{7} + q^{8} + 3 q^{9} + 2 q^{11} + 2 q^{12} - q^{16} + 4 q^{17} - 15 q^{18} - 16 q^{22} + 2 q^{23} + 4 q^{24} - q^{25} + 2 q^{26} - 14 q^{27} + 2 q^{28} + q^{32} + 4 q^{33} + 2 q^{34} + 3 q^{36} + 16 q^{39} + 2 q^{41} - 2 q^{42} + 2 q^{43} - 16 q^{44} - 4 q^{47} - 16 q^{48} + q^{49} + q^{50} - 14 q^{51} + 2 q^{54} - 16 q^{58} + 2 q^{59} - q^{64} + 4 q^{66} + 2 q^{67} - 14 q^{68} - 15 q^{72} - 14 q^{73} - 4 q^{74} + 2 q^{75} - 11 q^{81} + 2 q^{82} + 2 q^{83} + 2 q^{86} - 2 q^{87} + 2 q^{88} + 2 q^{89} + 2 q^{92} - 32 q^{96} + 2 q^{97} + q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2888))\)

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
2888.1.d \(\chi_{2888}(2167, \cdot)\) None 0 1
2888.1.e \(\chi_{2888}(721, \cdot)\) None 0 1
2888.1.f \(\chi_{2888}(723, \cdot)\) 2888.1.f.a 1 1
2888.1.f.b 1
2888.1.f.c 3
2888.1.f.d 3
2888.1.g \(\chi_{2888}(2165, \cdot)\) None 0 1
2888.1.k \(\chi_{2888}(2595, \cdot)\) 2888.1.k.a 2 2
2888.1.k.b 6
2888.1.k.c 6
2888.1.l \(\chi_{2888}(69, \cdot)\) 2888.1.l.a 2 2
2888.1.l.b 2
2888.1.m \(\chi_{2888}(1151, \cdot)\) None 0 2
2888.1.n \(\chi_{2888}(1513, \cdot)\) None 0 2
2888.1.r \(\chi_{2888}(849, \cdot)\) None 0 6
2888.1.s \(\chi_{2888}(333, \cdot)\) 2888.1.s.a 6 6
2888.1.s.b 6
2888.1.u \(\chi_{2888}(99, \cdot)\) 2888.1.u.a 6 6
2888.1.u.b 6
2888.1.u.c 6
2888.1.u.d 6
2888.1.u.e 6
2888.1.u.f 6
2888.1.u.g 6
2888.1.x \(\chi_{2888}(415, \cdot)\) None 0 6
2888.1.ba \(\chi_{2888}(37, \cdot)\) None 0 18
2888.1.bb \(\chi_{2888}(115, \cdot)\) 2888.1.bb.a 18 18
2888.1.bc \(\chi_{2888}(113, \cdot)\) None 0 18
2888.1.bd \(\chi_{2888}(39, \cdot)\) None 0 18
2888.1.bj \(\chi_{2888}(65, \cdot)\) None 0 36
2888.1.bk \(\chi_{2888}(7, \cdot)\) None 0 36
2888.1.bl \(\chi_{2888}(141, \cdot)\) None 0 36
2888.1.bm \(\chi_{2888}(11, \cdot)\) 2888.1.bm.a 36 36
2888.1.bp \(\chi_{2888}(23, \cdot)\) None 0 108
2888.1.bs \(\chi_{2888}(35, \cdot)\) 2888.1.bs.a 108 108
2888.1.bu \(\chi_{2888}(13, \cdot)\) None 0 108
2888.1.bv \(\chi_{2888}(33, \cdot)\) None 0 108

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2888))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2888)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1444))\)\(^{\oplus 2}\)