Properties

Label 385.2.t
Level $385$
Weight $2$
Character orbit 385.t
Rep. character $\chi_{385}(144,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $3$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 385 = 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 385.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 104 80 24
Cusp forms 88 80 8
Eisenstein series 16 0 16

Trace form

\( 80q + 40q^{4} - 8q^{6} + 36q^{9} + O(q^{10}) \) \( 80q + 40q^{4} - 8q^{6} + 36q^{9} - 6q^{10} - 28q^{14} - 28q^{15} - 36q^{16} - 8q^{19} - 24q^{20} - 12q^{24} + 4q^{25} + 16q^{26} + 48q^{29} - 16q^{30} + 12q^{31} - 24q^{34} + 14q^{35} - 24q^{36} - 24q^{39} + 64q^{40} + 8q^{41} - 4q^{44} + 6q^{45} - 28q^{46} + 24q^{49} - 16q^{50} - 24q^{51} - 4q^{54} + 48q^{56} - 44q^{59} - 36q^{60} + 20q^{61} - 40q^{64} - 18q^{65} + 16q^{66} - 32q^{69} + 6q^{70} + 16q^{71} - 24q^{74} - 12q^{75} + 56q^{76} - 32q^{79} - 50q^{80} + 48q^{81} - 156q^{84} - 24q^{85} + 76q^{86} - 84q^{89} - 188q^{90} + 80q^{91} + 56q^{94} - 16q^{95} - 84q^{96} + O(q^{100}) \)

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.t.a \(4\) \(3.074\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
385.2.t.b \(36\) \(3.074\) None \(0\) \(0\) \(2\) \(0\)
385.2.t.c \(40\) \(3.074\) None \(0\) \(0\) \(0\) \(0\)

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

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