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Properties

Label 385.2.bv
Level $385$
Weight $2$
Character orbit 385.bv
Rep. character $\chi_{385}(2,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $704$
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.bv (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{60})\)
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 832 832 0
Cusp forms 704 704 0
Eisenstein series 128 128 0

Trace form

\( 704 q - 10 q^{2} - 6 q^{3} - 2 q^{5} - 80 q^{6} - 30 q^{7} - 40 q^{8} + O(q^{10}) \) \( 704 q - 10 q^{2} - 6 q^{3} - 2 q^{5} - 80 q^{6} - 30 q^{7} - 40 q^{8} - 16 q^{11} - 40 q^{13} - 48 q^{15} - 68 q^{16} - 30 q^{17} - 10 q^{18} + 8 q^{20} - 32 q^{23} - 26 q^{25} - 36 q^{26} - 80 q^{28} - 10 q^{30} - 12 q^{31} + 32 q^{33} - 20 q^{35} + 176 q^{36} - 34 q^{37} - 22 q^{38} + 70 q^{40} - 200 q^{41} - 80 q^{42} + 56 q^{45} - 140 q^{46} + 34 q^{47} - 208 q^{48} - 40 q^{50} - 140 q^{51} - 10 q^{52} + 14 q^{53} - 56 q^{55} + 200 q^{56} - 200 q^{57} - 70 q^{58} + 14 q^{60} + 60 q^{61} - 40 q^{62} - 8 q^{66} + 32 q^{67} + 90 q^{68} + 76 q^{70} + 48 q^{71} - 70 q^{72} - 130 q^{73} + 58 q^{75} - 140 q^{77} - 8 q^{78} - 2 q^{80} - 72 q^{81} + 2 q^{82} - 40 q^{83} + 40 q^{85} - 52 q^{86} - 54 q^{88} + 460 q^{90} - 68 q^{91} - 136 q^{92} - 70 q^{93} - 160 q^{96} - 64 q^{97} + O(q^{100}) \)

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.bv.a 385.bv 385.av $704$ $3.074$ None \(-10\) \(-6\) \(-2\) \(-30\) $\mathrm{SU}(2)[C_{60}]$