Properties

Label 385.2.br
Level $385$
Weight $2$
Character orbit 385.br
Rep. character $\chi_{385}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $352$
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.br (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{30})\)
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 416 416 0
Cusp forms 352 352 0
Eisenstein series 64 64 0

Trace form

\( 352q + 34q^{4} - 15q^{5} + 36q^{9} + O(q^{10}) \) \( 352q + 34q^{4} - 15q^{5} + 36q^{9} - 6q^{11} - 18q^{14} - 36q^{15} + 30q^{16} - 30q^{19} - 30q^{24} + 23q^{25} - 54q^{26} - 40q^{29} - 35q^{30} - 54q^{31} - 25q^{35} - 52q^{36} + 30q^{39} - 105q^{40} - 22q^{44} - 60q^{45} - 110q^{46} - 58q^{49} - 20q^{50} + 50q^{51} + 68q^{56} + 6q^{59} + 15q^{60} - 120q^{64} + 150q^{66} - 53q^{70} + 8q^{71} - 80q^{74} - 27q^{75} - 10q^{79} - 195q^{80} + 60q^{81} + 10q^{84} - 130q^{85} - 2q^{86} + 12q^{89} - 98q^{91} - 180q^{94} - 50q^{95} + 420q^{96} - 80q^{99} + O(q^{100}) \)

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.br.a \(352\) \(3.074\) None \(0\) \(0\) \(-15\) \(0\)