Properties

Label 385.2.bd
Level $385$
Weight $2$
Character orbit 385.bd
Rep. character $\chi_{385}(12,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $160$
Newform subspaces $2$
Sturm bound $96$
Trace bound $8$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 385 = 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 385.bd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(8\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(385, [\chi])\).

Total New Old
Modular forms 208 160 48
Cusp forms 176 160 16
Eisenstein series 32 0 32

Trace form

\( 160q - 24q^{8} + O(q^{10}) \) \( 160q - 24q^{8} + 24q^{15} + 72q^{16} - 36q^{17} - 16q^{18} - 56q^{21} - 8q^{23} - 76q^{28} - 16q^{30} + 24q^{31} + 64q^{32} - 12q^{35} - 208q^{36} + 12q^{38} - 48q^{40} + 88q^{42} + 48q^{43} + 36q^{45} - 24q^{46} - 72q^{47} - 8q^{50} - 108q^{52} - 24q^{53} + 24q^{56} - 120q^{57} + 24q^{58} + 48q^{60} + 24q^{61} - 104q^{63} + 48q^{65} - 8q^{67} - 144q^{68} + 132q^{70} + 16q^{71} + 52q^{72} + 96q^{73} + 48q^{75} - 72q^{78} + 108q^{80} + 48q^{81} + 72q^{82} + 48q^{85} - 40q^{86} - 36q^{87} + 24q^{88} - 112q^{91} - 40q^{92} - 20q^{93} + 8q^{95} + 168q^{96} + 48q^{98} + O(q^{100}) \)

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.bd.a \(80\) \(3.074\) None \(0\) \(0\) \(0\) \(0\)
385.2.bd.b \(80\) \(3.074\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(385, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)