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Properties

Label 385.2.bk
Level $385$
Weight $2$
Character orbit 385.bk
Rep. character $\chi_{385}(27,\cdot)$
Character field $\Q(\zeta_{20})$
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.bk (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
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 416 416 0
Cusp forms 352 352 0
Eisenstein series 64 64 0

Trace form

\( 352 q - 12 q^{2} - 8 q^{7} - 28 q^{8} + O(q^{10}) \) \( 352 q - 12 q^{2} - 8 q^{7} - 28 q^{8} - 36 q^{11} - 36 q^{15} + 24 q^{16} - 52 q^{18} - 32 q^{21} - 24 q^{22} - 64 q^{23} + 20 q^{25} - 50 q^{28} - 68 q^{30} - 48 q^{32} + 10 q^{35} - 8 q^{36} + 28 q^{37} - 74 q^{42} + 8 q^{43} - 80 q^{46} + 52 q^{50} + 80 q^{51} - 52 q^{53} - 128 q^{56} + 124 q^{57} + 44 q^{58} + 28 q^{60} - 34 q^{63} + 128 q^{65} - 176 q^{67} + 22 q^{70} - 24 q^{71} + 4 q^{72} - 86 q^{77} - 216 q^{78} + 36 q^{81} + 108 q^{85} + 40 q^{86} - 4 q^{88} + 40 q^{91} - 28 q^{92} - 140 q^{93} + 120 q^{95} + 128 q^{98} + O(q^{100}) \)

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.bk.a 385.bk 385.ak $352$ $3.074$ None \(-12\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{20}]$