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Properties

Label 3513.1
Level 3513
Weight 1
Dimension 206
Nonzero newspaces 7
Newform subspaces 9
Sturm bound 914160
Trace bound 3

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Defining parameters

Level: \( N \) = \( 3513 = 3 \cdot 1171 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 9 \)
Sturm bound: \(914160\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3513))\).

Total New Old
Modular forms 2552 1374 1178
Cusp forms 212 206 6
Eisenstein series 2340 1168 1172

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 194 0 4 8

Trace form

\( 206 q + q^{3} + q^{4} - 2 q^{6} - 4 q^{7} - 11 q^{9} + O(q^{10}) \) \( 206 q + q^{3} + q^{4} - 2 q^{6} - 4 q^{7} - 11 q^{9} - 4 q^{10} - 3 q^{12} + 6 q^{13} + 3 q^{16} + 2 q^{21} - 2 q^{22} - 2 q^{24} - q^{25} - 5 q^{27} + 2 q^{28} + 4 q^{30} - 8 q^{31} - 4 q^{33} - 8 q^{34} - 5 q^{36} + 2 q^{39} + 6 q^{42} - 8 q^{43} - 6 q^{46} + 3 q^{48} + q^{49} + 2 q^{52} + 2 q^{54} - 4 q^{55} - 2 q^{57} + 6 q^{58} - 4 q^{61} + 4 q^{63} + 5 q^{64} + 8 q^{66} - 4 q^{67} - 4 q^{69} - 8 q^{70} - 3 q^{75} - 2 q^{76} + 4 q^{79} + 5 q^{81} - 2 q^{82} + 8 q^{85} - 8 q^{87} + 4 q^{88} + 8 q^{90} - 6 q^{93} - 8 q^{94} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3513))\)

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
3513.1.b \(\chi_{3513}(1172, \cdot)\) None 0 1
3513.1.c \(\chi_{3513}(2341, \cdot)\) None 0 1
3513.1.h \(\chi_{3513}(421, \cdot)\) None 0 2
3513.1.i \(\chi_{3513}(2762, \cdot)\) 3513.1.i.a 2 2
3513.1.i.b 4
3513.1.l \(\chi_{3513}(103, \cdot)\) None 0 4
3513.1.m \(\chi_{3513}(1241, \cdot)\) 3513.1.m.a 4 4
3513.1.m.b 8
3513.1.q \(\chi_{3513}(388, \cdot)\) None 0 6
3513.1.r \(\chi_{3513}(335, \cdot)\) None 0 6
3513.1.t \(\chi_{3513}(86, \cdot)\) 3513.1.t.a 12 12
3513.1.u \(\chi_{3513}(643, \cdot)\) None 0 12
3513.1.v \(\chi_{3513}(125, \cdot)\) 3513.1.v.a 8 8
3513.1.w \(\chi_{3513}(769, \cdot)\) None 0 8
3513.1.bb \(\chi_{3513}(181, \cdot)\) None 0 24
3513.1.bc \(\chi_{3513}(20, \cdot)\) 3513.1.bc.a 24 24
3513.1.be \(\chi_{3513}(91, \cdot)\) None 0 24
3513.1.bf \(\chi_{3513}(5, \cdot)\) None 0 24
3513.1.bi \(\chi_{3513}(97, \cdot)\) None 0 48
3513.1.bj \(\chi_{3513}(41, \cdot)\) 3513.1.bj.a 48 48
3513.1.bm \(\chi_{3513}(59, \cdot)\) None 0 72
3513.1.bn \(\chi_{3513}(7, \cdot)\) None 0 72
3513.1.bq \(\chi_{3513}(23, \cdot)\) 3513.1.bq.a 96 96
3513.1.br \(\chi_{3513}(28, \cdot)\) None 0 96
3513.1.bu \(\chi_{3513}(17, \cdot)\) None 0 288
3513.1.bv \(\chi_{3513}(10, \cdot)\) None 0 288

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3513))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3513)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3513))\)\(^{\oplus 1}\)