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 $0$

Related objects

Downloads

Learn more

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

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

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.bk.a \(352\) \(3.074\) None \(-12\) \(0\) \(0\) \(-8\)