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Properties

Label 385.2.bj
Level $385$
Weight $2$
Character orbit 385.bj
Rep. character $\chi_{385}(8,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $288$
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.bj (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
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 416 288 128
Cusp forms 352 288 64
Eisenstein series 64 0 64

Trace form

\( 288 q - 4 q^{3} + O(q^{10}) \) \( 288 q - 4 q^{3} + 4 q^{11} - 96 q^{12} - 16 q^{15} + 72 q^{16} - 76 q^{20} - 44 q^{22} - 16 q^{23} - 12 q^{25} - 64 q^{26} - 4 q^{27} - 80 q^{30} + 32 q^{31} - 32 q^{33} - 56 q^{36} - 4 q^{37} - 16 q^{38} + 48 q^{45} - 40 q^{46} + 16 q^{47} + 136 q^{48} + 80 q^{50} - 80 q^{51} + 80 q^{52} + 76 q^{53} + 112 q^{55} - 48 q^{56} + 80 q^{57} + 32 q^{58} - 40 q^{60} - 220 q^{62} + 16 q^{66} + 128 q^{67} - 16 q^{70} - 72 q^{71} - 300 q^{72} + 48 q^{75} - 8 q^{77} - 64 q^{78} - 80 q^{80} + 60 q^{81} + 24 q^{82} - 200 q^{83} - 40 q^{85} - 160 q^{86} - 352 q^{88} - 36 q^{91} + 236 q^{92} + 68 q^{93} + 80 q^{95} - 320 q^{96} + 44 q^{97} + O(q^{100}) \)

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.bj.a 385.bj 55.l $288$ $3.074$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$

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

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