Properties

Label 342.2.s
Level $342$
Weight $2$
Character orbit 342.s
Rep. character $\chi_{342}(107,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $2$
Sturm bound $120$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 342.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(342, [\chi])\).

Total New Old
Modular forms 136 8 128
Cusp forms 104 8 96
Eisenstein series 32 0 32

Trace form

\( 8q - 4q^{4} - 8q^{7} + O(q^{10}) \) \( 8q - 4q^{4} - 8q^{7} + 12q^{13} - 4q^{16} + 32q^{19} - 24q^{22} - 12q^{25} + 4q^{28} - 24q^{34} + 4q^{43} - 12q^{52} - 16q^{55} + 4q^{61} + 8q^{64} - 12q^{67} + 24q^{70} + 28q^{73} - 4q^{76} + 36q^{79} + 8q^{85} + 60q^{91} - 72q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(342, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
342.2.s.a \(4\) \(2.731\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(0\) \(0\) \(-4\) \(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
342.2.s.b \(4\) \(2.731\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(-4\) \(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

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