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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
385.2.br.a 385.br 385.ar $352$ $3.074$ None \(0\) \(0\) \(-15\) \(0\) $\mathrm{SU}(2)[C_{30}]$