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Properties

Label 3249.1
Level 3249
Weight 1
Dimension 128
Nonzero newspaces 12
Newform subspaces 15
Sturm bound 779760
Trace bound 7

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Defining parameters

Level: \( N \) = \( 3249 = 3^{2} \cdot 19^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 15 \)
Sturm bound: \(779760\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3249))\).

Total New Old
Modular forms 4322 2236 2086
Cusp forms 290 128 162
Eisenstein series 4032 2108 1924

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 96 32 0 0

Trace form

\( 128 q + 2 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{9} + O(q^{10}) \) \( 128 q + 2 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{9} - 2 q^{11} + 6 q^{13} - 2 q^{16} + 3 q^{19} - 2 q^{23} - 4 q^{24} + 4 q^{26} + 6 q^{28} - 4 q^{30} - 4 q^{35} - 16 q^{39} + 2 q^{42} - 4 q^{43} - 2 q^{45} + 2 q^{47} - 6 q^{49} - 6 q^{52} - 2 q^{54} + 4 q^{55} - 16 q^{58} + 4 q^{61} - 4 q^{62} - 2 q^{63} - 2 q^{64} - 2 q^{66} - 6 q^{67} - 6 q^{73} + 16 q^{77} + 6 q^{79} + 4 q^{80} - 4 q^{81} + 4 q^{82} - 2 q^{83} - 2 q^{87} + 6 q^{91} - 2 q^{93} + 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3249))\)

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
3249.1.b \(\chi_{3249}(2528, \cdot)\) 3249.1.b.a 2 1
3249.1.c \(\chi_{3249}(721, \cdot)\) 3249.1.c.a 2 1
3249.1.i \(\chi_{3249}(430, \cdot)\) 3249.1.i.a 4 2
3249.1.j \(\chi_{3249}(68, \cdot)\) None 0 2
3249.1.n \(\chi_{3249}(653, \cdot)\) None 0 2
3249.1.o \(\chi_{3249}(1804, \cdot)\) None 0 2
3249.1.p \(\chi_{3249}(1513, \cdot)\) 3249.1.p.a 2 2
3249.1.p.b 2
3249.1.q \(\chi_{3249}(362, \cdot)\) None 0 2
3249.1.r \(\chi_{3249}(1151, \cdot)\) 3249.1.r.a 4 2
3249.1.s \(\chi_{3249}(1015, \cdot)\) 3249.1.s.a 4 2
3249.1.z \(\chi_{3249}(389, \cdot)\) None 0 6
3249.1.ba \(\chi_{3249}(127, \cdot)\) 3249.1.ba.a 6 6
3249.1.ba.b 6
3249.1.ba.c 6
3249.1.bb \(\chi_{3249}(62, \cdot)\) 3249.1.bb.a 12 6
3249.1.bc \(\chi_{3249}(1021, \cdot)\) 3249.1.bc.a 12 6
3249.1.be \(\chi_{3249}(1210, \cdot)\) 3249.1.be.a 12 6
3249.1.bf \(\chi_{3249}(245, \cdot)\) None 0 6
3249.1.bi \(\chi_{3249}(37, \cdot)\) 3249.1.bi.a 18 18
3249.1.bj \(\chi_{3249}(134, \cdot)\) None 0 18
3249.1.bp \(\chi_{3249}(31, \cdot)\) None 0 36
3249.1.bq \(\chi_{3249}(26, \cdot)\) None 0 36
3249.1.br \(\chi_{3249}(20, \cdot)\) None 0 36
3249.1.bs \(\chi_{3249}(46, \cdot)\) 3249.1.bs.a 36 36
3249.1.bt \(\chi_{3249}(94, \cdot)\) None 0 36
3249.1.bu \(\chi_{3249}(11, \cdot)\) None 0 36
3249.1.by \(\chi_{3249}(83, \cdot)\) None 0 36
3249.1.bz \(\chi_{3249}(88, \cdot)\) None 0 36
3249.1.cd \(\chi_{3249}(23, \cdot)\) None 0 108
3249.1.ce \(\chi_{3249}(13, \cdot)\) None 0 108
3249.1.cg \(\chi_{3249}(22, \cdot)\) None 0 108
3249.1.ch \(\chi_{3249}(17, \cdot)\) None 0 108
3249.1.ci \(\chi_{3249}(10, \cdot)\) None 0 108
3249.1.cj \(\chi_{3249}(5, \cdot)\) None 0 108

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3249))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3249)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 2}\)