Properties

Label 385.2.bb
Level $385$
Weight $2$
Character orbit 385.bb
Rep. character $\chi_{385}(64,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $144$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 385 = 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 385.bb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(385, [\chi])\).

Total New Old
Modular forms 208 144 64
Cusp forms 176 144 32
Eisenstein series 32 0 32

Trace form

\( 144q + 36q^{4} + 2q^{5} + 26q^{9} + O(q^{10}) \) \( 144q + 36q^{4} + 2q^{5} + 26q^{9} - 16q^{10} - 2q^{11} + 2q^{15} - 84q^{16} - 16q^{19} + 22q^{20} - 36q^{21} + 32q^{24} - 6q^{25} - 92q^{26} - 20q^{29} - 20q^{30} - 4q^{31} + 16q^{34} + 12q^{36} - 36q^{39} - 46q^{40} - 52q^{44} - 40q^{45} + 92q^{46} + 36q^{49} - 38q^{50} + 4q^{51} - 128q^{54} + 34q^{55} - 24q^{56} - 40q^{59} + 12q^{60} + 32q^{61} + 132q^{64} + 28q^{65} + 52q^{66} - 44q^{69} + 4q^{70} - 28q^{71} + 16q^{74} - 30q^{75} + 104q^{76} - 52q^{79} + 8q^{80} - 82q^{81} - 48q^{84} - 40q^{85} + 72q^{86} - 64q^{89} - 292q^{90} + 18q^{91} - 12q^{94} - 56q^{95} + 216q^{96} + 216q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(385, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
385.2.bb.a \(144\) \(3.074\) None \(0\) \(0\) \(2\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(385, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(385, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)