Properties

Label 1380.2.p
Level $1380$
Weight $2$
Character orbit 1380.p
Rep. character $\chi_{1380}(91,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $2$
Sturm bound $576$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1380.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1380, [\chi])\).

Total New Old
Modular forms 296 96 200
Cusp forms 280 96 184
Eisenstein series 16 0 16

Trace form

\( 96q - 8q^{2} - 4q^{4} - 4q^{6} - 8q^{8} - 96q^{9} + O(q^{10}) \) \( 96q - 8q^{2} - 4q^{4} - 4q^{6} - 8q^{8} - 96q^{9} - 12q^{16} + 8q^{18} + 4q^{24} - 96q^{25} - 40q^{26} + 64q^{29} + 32q^{32} + 4q^{36} - 16q^{41} + 40q^{46} + 32q^{48} + 80q^{49} + 8q^{50} - 32q^{52} + 4q^{54} - 16q^{58} + 48q^{62} - 52q^{64} - 16q^{69} + 8q^{72} + 64q^{77} + 96q^{81} - 40q^{82} + 32q^{85} - 32q^{92} - 64q^{94} - 4q^{96} + 48q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1380.2.p.a \(48\) \(11.019\) None \(-4\) \(0\) \(0\) \(0\)
1380.2.p.b \(48\) \(11.019\) None \(-4\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)