Properties

Label 385.2.j
Level $385$
Weight $2$
Character orbit 385.j
Rep. character $\chi_{385}(188,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $80$
Newform subspaces $4$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 385 = 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 385.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

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

\( 80q + 24q^{8} + O(q^{10}) \) \( 80q + 24q^{8} - 24q^{15} - 96q^{16} + 16q^{18} + 32q^{21} + 8q^{23} - 20q^{28} + 88q^{30} + 8q^{32} - 60q^{35} - 32q^{36} - 16q^{42} - 24q^{43} - 48q^{46} - 112q^{50} + 24q^{53} - 24q^{57} + 72q^{58} + 72q^{60} + 20q^{63} - 48q^{65} - 16q^{67} + 48q^{70} + 32q^{71} + 128q^{72} + 96q^{78} - 144q^{81} - 48q^{85} - 128q^{86} - 24q^{88} - 80q^{91} + 88q^{92} - 40q^{93} - 80q^{95} + 96q^{98} + O(q^{100}) \)

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.j.a \(4\) \(3.074\) \(\Q(\zeta_{12})\) None \(-4\) \(-6\) \(-2\) \(-8\) \(q+(-1-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
385.2.j.b \(4\) \(3.074\) \(\Q(\zeta_{12})\) None \(-4\) \(6\) \(2\) \(0\) \(q+(-1+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
385.2.j.c \(32\) \(3.074\) None \(8\) \(0\) \(0\) \(8\)
385.2.j.d \(40\) \(3.074\) None \(0\) \(0\) \(0\) \(0\)

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

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