Properties

Label 385.2.i
Level $385$
Weight $2$
Character orbit 385.i
Rep. character $\chi_{385}(221,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $56$
Newform subspaces $4$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
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 56 48
Cusp forms 88 56 32
Eisenstein series 16 0 16

Trace form

\( 56q + 4q^{3} - 32q^{4} + 4q^{5} + 8q^{6} - 4q^{7} - 36q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 32q^{4} + 4q^{5} + 8q^{6} - 4q^{7} - 36q^{9} - 12q^{12} + 32q^{13} + 4q^{14} - 44q^{16} - 20q^{18} + 4q^{19} - 16q^{20} - 20q^{21} + 28q^{24} - 28q^{25} - 12q^{26} - 32q^{27} + 20q^{28} + 32q^{29} - 4q^{30} - 24q^{31} - 40q^{32} + 8q^{33} + 24q^{34} + 4q^{35} + 160q^{36} - 8q^{37} + 44q^{38} - 12q^{39} - 8q^{41} + 48q^{42} - 24q^{43} - 4q^{44} - 16q^{46} + 12q^{47} - 32q^{48} + 24q^{49} - 8q^{51} - 40q^{52} + 12q^{53} - 48q^{54} - 16q^{55} - 84q^{56} - 8q^{57} - 20q^{58} - 4q^{59} - 4q^{61} + 56q^{62} - 28q^{63} + 128q^{64} - 20q^{66} + 8q^{67} + 16q^{68} - 24q^{69} + 4q^{70} - 24q^{71} + 16q^{72} + 4q^{73} + 40q^{74} + 4q^{75} + 8q^{76} + 4q^{77} - 136q^{78} + 16q^{79} + 20q^{80} - 52q^{81} + 12q^{82} + 112q^{83} + 12q^{84} + 8q^{85} - 64q^{86} + 48q^{87} - 40q^{89} + 72q^{90} + 12q^{91} + 36q^{93} - 12q^{94} + 56q^{96} - 120q^{97} + 52q^{98} + O(q^{100}) \)

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.i.a \(8\) \(3.074\) 8.0.310217769.2 None \(3\) \(3\) \(-4\) \(1\) \(q+(1+\beta _{1}+\beta _{2}-\beta _{5}-\beta _{7})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots\)
385.2.i.b \(12\) \(3.074\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(-1\) \(6\) \(-3\) \(q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{9}q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
385.2.i.c \(16\) \(3.074\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-3\) \(-1\) \(-8\) \(-1\) \(q-\beta _{1}q^{2}+(-\beta _{4}+\beta _{7})q^{3}+(-\beta _{8}+\beta _{11}+\cdots)q^{4}+\cdots\)
385.2.i.d \(20\) \(3.074\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-3\) \(3\) \(10\) \(-1\) \(q-\beta _{1}q^{2}+(-\beta _{10}+\beta _{17})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(385, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)