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Properties

Label 1340.1
Level 1340
Weight 1
Dimension 64
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 107712
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(107712\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1340))\).

Total New Old
Modular forms 1410 456 954
Cusp forms 90 64 26
Eisenstein series 1320 392 928

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 64 0 0 0

Trace form

\( 64 q - 2 q^{4} - 2 q^{5} - 4 q^{6} - 6 q^{9} + O(q^{10}) \) \( 64 q - 2 q^{4} - 2 q^{5} - 4 q^{6} - 6 q^{9} - 4 q^{14} - 2 q^{16} - 2 q^{20} - 8 q^{21} - 4 q^{24} - 2 q^{25} - 4 q^{29} - 4 q^{30} - 6 q^{36} - 4 q^{41} - 6 q^{45} - 4 q^{46} - 6 q^{49} - 8 q^{54} - 4 q^{56} - 4 q^{61} - 2 q^{64} - 8 q^{69} - 4 q^{70} - 2 q^{80} - 10 q^{81} - 8 q^{84} - 4 q^{86} - 4 q^{89} - 4 q^{94} - 4 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1340))\)

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
1340.1.b \(\chi_{1340}(401, \cdot)\) None 0 1
1340.1.c \(\chi_{1340}(671, \cdot)\) None 0 1
1340.1.f \(\chi_{1340}(939, \cdot)\) None 0 1
1340.1.g \(\chi_{1340}(669, \cdot)\) None 0 1
1340.1.l \(\chi_{1340}(537, \cdot)\) None 0 2
1340.1.m \(\chi_{1340}(267, \cdot)\) None 0 2
1340.1.p \(\chi_{1340}(171, \cdot)\) None 0 2
1340.1.q \(\chi_{1340}(641, \cdot)\) None 0 2
1340.1.s \(\chi_{1340}(909, \cdot)\) None 0 2
1340.1.t \(\chi_{1340}(439, \cdot)\) 1340.1.t.a 2 2
1340.1.t.b 2
1340.1.v \(\chi_{1340}(507, \cdot)\) None 0 4
1340.1.w \(\chi_{1340}(37, \cdot)\) None 0 4
1340.1.ba \(\chi_{1340}(109, \cdot)\) None 0 10
1340.1.bb \(\chi_{1340}(59, \cdot)\) 1340.1.bb.a 10 10
1340.1.bb.b 10
1340.1.be \(\chi_{1340}(91, \cdot)\) None 0 10
1340.1.bf \(\chi_{1340}(161, \cdot)\) None 0 10
1340.1.bh \(\chi_{1340}(3, \cdot)\) None 0 20
1340.1.bi \(\chi_{1340}(193, \cdot)\) None 0 20
1340.1.bl \(\chi_{1340}(19, \cdot)\) 1340.1.bl.a 20 20
1340.1.bl.b 20
1340.1.bm \(\chi_{1340}(69, \cdot)\) None 0 20
1340.1.bo \(\chi_{1340}(41, \cdot)\) None 0 20
1340.1.bp \(\chi_{1340}(71, \cdot)\) None 0 20
1340.1.bu \(\chi_{1340}(17, \cdot)\) None 0 40
1340.1.bv \(\chi_{1340}(7, \cdot)\) None 0 40

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1340))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1340)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(268))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(335))\)\(^{\oplus 3}\)