Properties

Label 385.2.bg
Level $385$
Weight $2$
Character orbit 385.bg
Rep. character $\chi_{385}(16,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $256$
Newform subspaces $2$
Sturm bound $96$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 385 = 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 385.bg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 416 256 160
Cusp forms 352 256 96
Eisenstein series 64 0 64

Trace form

\( 256q + 4q^{2} + 36q^{4} + 16q^{8} + 26q^{9} + O(q^{10}) \) \( 256q + 4q^{2} + 36q^{4} + 16q^{8} + 26q^{9} - 16q^{10} + 4q^{11} - 16q^{13} - 6q^{14} + 12q^{15} + 36q^{16} + 28q^{17} - 46q^{18} - 4q^{19} + 8q^{20} - 8q^{21} - 112q^{22} - 4q^{23} + 36q^{24} + 32q^{25} + 28q^{26} - 36q^{27} + 24q^{28} - 64q^{29} + 8q^{32} + 4q^{33} - 192q^{34} + 4q^{35} - 96q^{36} - 32q^{37} - 28q^{38} - 20q^{39} + 12q^{40} - 72q^{41} + 136q^{42} - 16q^{43} - 18q^{44} + 10q^{46} - 4q^{47} - 212q^{48} + 16q^{49} - 8q^{50} - 20q^{51} - 28q^{53} + 60q^{54} + 8q^{55} - 52q^{56} + 40q^{57} + 6q^{58} - 12q^{59} + 58q^{60} - 48q^{61} + 72q^{62} + 8q^{63} - 112q^{64} - 8q^{65} + 16q^{66} + 56q^{67} + 84q^{68} + 248q^{69} - 44q^{70} - 64q^{71} + 38q^{72} + 34q^{73} + 70q^{74} - 72q^{76} - 32q^{77} + 80q^{78} - 38q^{79} - 8q^{80} + 78q^{81} - 8q^{82} + 84q^{84} - 24q^{85} - 74q^{86} - 192q^{87} - 36q^{88} + 48q^{89} - 40q^{90} - 86q^{91} + 116q^{92} - 30q^{93} - 150q^{94} - 6q^{96} + 72q^{97} - 24q^{98} + 88q^{99} + O(q^{100}) \)

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.bg.a \(128\) \(3.074\) None \(0\) \(3\) \(-16\) \(-6\)
385.2.bg.b \(128\) \(3.074\) None \(4\) \(-3\) \(16\) \(6\)

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

\( S_{2}^{\mathrm{old}}(385, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)