Properties

Label 1340.1.bl
Level $1340$
Weight $1$
Character orbit 1340.bl
Rep. character $\chi_{1340}(19,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $40$
Newform subspaces $2$
Sturm bound $204$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1340.bl (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1340 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 2 \)
Sturm bound: \(204\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1340, [\chi])\).

Total New Old
Modular forms 120 120 0
Cusp forms 40 40 0
Eisenstein series 80 80 0

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

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

Trace form

\( 40q + 2q^{4} - 4q^{5} - 2q^{6} + O(q^{10}) \) \( 40q + 2q^{4} - 4q^{5} - 2q^{6} + 4q^{14} + 2q^{16} + 2q^{20} - 20q^{21} - 18q^{24} - 4q^{25} - 2q^{29} - 2q^{30} - 2q^{41} - 2q^{46} + 2q^{54} - 2q^{56} - 18q^{61} - 4q^{64} + 2q^{69} - 18q^{70} + 2q^{80} + 4q^{81} + 2q^{84} - 2q^{86} - 8q^{89} + 4q^{94} - 2q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1340, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1340.1.bl.a \(20\) \(0.669\) \(\Q(\zeta_{33})\) \(D_{33}\) \(\Q(\sqrt{-5}) \) None \(-1\) \(-2\) \(-2\) \(1\) \(q+\zeta_{66}^{31}q^{2}+(\zeta_{66}^{17}+\zeta_{66}^{25})q^{3}+\cdots\)
1340.1.bl.b \(20\) \(0.669\) \(\Q(\zeta_{33})\) \(D_{33}\) \(\Q(\sqrt{-5}) \) None \(1\) \(2\) \(-2\) \(-1\) \(q-\zeta_{66}^{31}q^{2}+(-\zeta_{66}^{17}-\zeta_{66}^{25}+\cdots)q^{3}+\cdots\)