↑

Properties

Label 3087.1
Level 3087
Weight 1
Dimension 135
Nonzero newspaces 7
Newform subspaces 10
Sturm bound 691488
Trace bound 4

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 3087 = 3^{2} \cdot 7^{3} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 10 \)
Sturm bound: \(691488\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3087))\).

Total New Old
Modular forms 4729 2079 2650
Cusp forms 361 135 226
Eisenstein series 4368 1944 2424

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 135 0 0 0

Trace form

\( 135 q - q^{4} + 6 q^{8} + O(q^{10}) \) \( 135 q - q^{4} + 6 q^{8} + q^{16} + 6 q^{22} + q^{25} + 3 q^{29} + 12 q^{37} + 13 q^{43} + 3 q^{50} + 14 q^{52} + 14 q^{61} - 19 q^{64} + 2 q^{67} + 3 q^{71} + 2 q^{79} - 12 q^{92} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3087))\)

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
3087.1.b \(\chi_{3087}(2402, \cdot)\) 3087.1.b.a 12 1
3087.1.d \(\chi_{3087}(685, \cdot)\) 3087.1.d.a 3 1
3087.1.d.b 6
3087.1.j \(\chi_{3087}(704, \cdot)\) None 0 2
3087.1.k \(\chi_{3087}(1354, \cdot)\) None 0 2
3087.1.l \(\chi_{3087}(1714, \cdot)\) None 0 2
3087.1.m \(\chi_{3087}(19, \cdot)\) 3087.1.m.a 6 2
3087.1.m.b 12
3087.1.n \(\chi_{3087}(1010, \cdot)\) None 0 2
3087.1.q \(\chi_{3087}(2762, \cdot)\) 3087.1.q.a 24 2
3087.1.r \(\chi_{3087}(344, \cdot)\) None 0 2
3087.1.t \(\chi_{3087}(1048, \cdot)\) None 0 2
3087.1.v \(\chi_{3087}(244, \cdot)\) 3087.1.v.a 6 6
3087.1.x \(\chi_{3087}(197, \cdot)\) None 0 6
3087.1.bc \(\chi_{3087}(166, \cdot)\) None 0 12
3087.1.be \(\chi_{3087}(50, \cdot)\) None 0 12
3087.1.bf \(\chi_{3087}(116, \cdot)\) None 0 12
3087.1.bi \(\chi_{3087}(128, \cdot)\) None 0 12
3087.1.bj \(\chi_{3087}(460, \cdot)\) 3087.1.bj.a 12 12
3087.1.bj.b 12
3087.1.bk \(\chi_{3087}(97, \cdot)\) None 0 12
3087.1.bl \(\chi_{3087}(31, \cdot)\) None 0 12
3087.1.bm \(\chi_{3087}(263, \cdot)\) None 0 12
3087.1.bp \(\chi_{3087}(55, \cdot)\) 3087.1.bp.a 42 42
3087.1.br \(\chi_{3087}(8, \cdot)\) None 0 42
3087.1.bx \(\chi_{3087}(13, \cdot)\) None 0 84
3087.1.by \(\chi_{3087}(11, \cdot)\) None 0 84
3087.1.bz \(\chi_{3087}(2, \cdot)\) None 0 84
3087.1.ca \(\chi_{3087}(44, \cdot)\) None 0 84
3087.1.cb \(\chi_{3087}(10, \cdot)\) None 0 84
3087.1.cd \(\chi_{3087}(61, \cdot)\) None 0 84
3087.1.cg \(\chi_{3087}(40, \cdot)\) None 0 84
3087.1.ch \(\chi_{3087}(29, \cdot)\) None 0 84

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3087))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3087)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(343))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1029))\)\(^{\oplus 2}\)