Properties

Label 342.3.d
Level $342$
Weight $3$
Character orbit 342.d
Rep. character $\chi_{342}(37,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $3$
Sturm bound $180$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 342.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(180\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(342, [\chi])\).

Total New Old
Modular forms 128 18 110
Cusp forms 112 18 94
Eisenstein series 16 0 16

Trace form

\( 18q - 36q^{4} - 2q^{5} + 10q^{7} + O(q^{10}) \) \( 18q - 36q^{4} - 2q^{5} + 10q^{7} - 14q^{11} + 72q^{16} + 46q^{17} - 10q^{19} + 4q^{20} + 76q^{23} + 64q^{25} + 48q^{26} - 20q^{28} - 226q^{35} - 48q^{38} + 114q^{43} + 28q^{44} + 178q^{47} + 168q^{49} - 194q^{55} + 24q^{58} - 146q^{61} - 24q^{62} - 144q^{64} - 92q^{68} + 102q^{73} + 120q^{74} + 20q^{76} - 118q^{77} - 8q^{80} - 120q^{82} + 124q^{83} - 134q^{85} - 152q^{92} + 178q^{95} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(342, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
342.3.d.a \(2\) \(9.319\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(2\) \(10\) \(q-\beta q^{2}-2q^{4}+q^{5}+5q^{7}+2\beta q^{8}+\cdots\)
342.3.d.b \(8\) \(9.319\) 8.0.\(\cdots\).3 None \(0\) \(0\) \(-4\) \(-12\) \(q+\beta _{2}q^{2}-2q^{4}-\beta _{5}q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
342.3.d.c \(8\) \(9.319\) 8.0.\(\cdots\).9 None \(0\) \(0\) \(0\) \(12\) \(q-\beta _{3}q^{2}-2q^{4}-\beta _{1}q^{5}+(1+\beta _{6})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(342, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)