Properties

Label 385.2.b
Level $385$
Weight $2$
Character orbit 385.b
Rep. character $\chi_{385}(309,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $4$
Sturm bound $96$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 385 = 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 385.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(2\), \(13\)

Dimensions

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

Total New Old
Modular forms 52 32 20
Cusp forms 44 32 12
Eisenstein series 8 0 8

Trace form

\( 32q - 28q^{4} + 6q^{5} - 8q^{6} - 44q^{9} + O(q^{10}) \) \( 32q - 28q^{4} + 6q^{5} - 8q^{6} - 44q^{9} + 8q^{10} + 8q^{11} - 8q^{14} + 2q^{15} + 20q^{16} + 16q^{19} + 12q^{20} - 32q^{24} - 6q^{25} - 16q^{26} + 16q^{30} - 4q^{31} + 40q^{34} + 4q^{35} + 84q^{36} - 24q^{40} - 8q^{41} - 20q^{44} - 24q^{45} - 40q^{46} - 32q^{49} + 40q^{50} + 8q^{51} - 72q^{54} - 6q^{55} + 24q^{56} + 20q^{59} + 60q^{60} - 4q^{64} - 24q^{65} + 28q^{69} + 12q^{70} + 20q^{71} - 66q^{75} - 104q^{76} - 8q^{79} - 40q^{80} + 88q^{81} - 28q^{85} + 80q^{86} - 36q^{89} + 16q^{90} + 16q^{91} + 128q^{94} - 44q^{95} - 24q^{96} - 4q^{99} + O(q^{100}) \)

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.b.a \(2\) \(3.074\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}-2iq^{3}+q^{4}+(1+2i)q^{5}+\cdots\)
385.2.b.b \(2\) \(3.074\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}-2iq^{3}+q^{4}+(1-2i)q^{5}+\cdots\)
385.2.b.c \(12\) \(3.074\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(6\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{2}-\beta _{10})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
385.2.b.d \(16\) \(3.074\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{7}+\beta _{13})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(385, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)