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Properties

Label 3267.1
Level 3267
Weight 1
Dimension 152
Nonzero newspaces 11
Newform subspaces 20
Sturm bound 784080
Trace bound 20

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Defining parameters

Level: \( N \) = \( 3267 = 3^{3} \cdot 11^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 11 \)
Newform subspaces: \( 20 \)
Sturm bound: \(784080\)
Trace bound: \(20\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3267))\).

Total New Old
Modular forms 5087 2400 2687
Cusp forms 287 152 135
Eisenstein series 4800 2248 2552

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 112 0 40 0

Trace form

\( 152 q + q^{4} + 4 q^{5} + O(q^{10}) \) \( 152 q + q^{4} + 4 q^{5} + 3 q^{15} + q^{16} - 5 q^{20} + 8 q^{23} + 3 q^{25} + 3 q^{27} + 2 q^{31} - 40 q^{34} - 6 q^{36} + 2 q^{37} + 4 q^{47} + 3 q^{48} + q^{49} - 2 q^{53} + 4 q^{59} + q^{64} - 17 q^{67} - 2 q^{71} - 6 q^{75} - 2 q^{80} - 49 q^{89} - 2 q^{92} - 6 q^{93} - 7 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3267))\)

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
3267.1.b \(\chi_{3267}(485, \cdot)\) 3267.1.b.a 1 1
3267.1.b.b 1
3267.1.b.c 2
3267.1.b.d 2
3267.1.b.e 2
3267.1.c \(\chi_{3267}(2782, \cdot)\) 3267.1.c.a 4 1
3267.1.h \(\chi_{3267}(604, \cdot)\) 3267.1.h.a 4 2
3267.1.i \(\chi_{3267}(1574, \cdot)\) 3267.1.i.a 2 2
3267.1.l \(\chi_{3267}(838, \cdot)\) 3267.1.l.a 16 4
3267.1.m \(\chi_{3267}(269, \cdot)\) 3267.1.m.a 4 4
3267.1.m.b 4
3267.1.m.c 8
3267.1.m.d 8
3267.1.m.e 8
3267.1.q \(\chi_{3267}(122, \cdot)\) 3267.1.q.a 6 6
3267.1.r \(\chi_{3267}(241, \cdot)\) None 0 6
3267.1.t \(\chi_{3267}(109, \cdot)\) None 0 10
3267.1.u \(\chi_{3267}(188, \cdot)\) None 0 10
3267.1.v \(\chi_{3267}(251, \cdot)\) 3267.1.v.a 8 8
3267.1.w \(\chi_{3267}(118, \cdot)\) 3267.1.w.a 8 8
3267.1.w.b 16
3267.1.bb \(\chi_{3267}(89, \cdot)\) None 0 20
3267.1.bc \(\chi_{3267}(10, \cdot)\) None 0 20
3267.1.be \(\chi_{3267}(245, \cdot)\) 3267.1.be.a 24 24
3267.1.bf \(\chi_{3267}(40, \cdot)\) 3267.1.bf.a 24 24
3267.1.bi \(\chi_{3267}(26, \cdot)\) None 0 40
3267.1.bj \(\chi_{3267}(28, \cdot)\) None 0 40
3267.1.bm \(\chi_{3267}(43, \cdot)\) None 0 60
3267.1.bn \(\chi_{3267}(23, \cdot)\) None 0 60
3267.1.bq \(\chi_{3267}(19, \cdot)\) None 0 80
3267.1.br \(\chi_{3267}(71, \cdot)\) None 0 80
3267.1.bu \(\chi_{3267}(7, \cdot)\) None 0 240
3267.1.bv \(\chi_{3267}(5, \cdot)\) None 0 240

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3267))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3267)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1089))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3267))\)\(^{\oplus 1}\)