Properties

Label 342.3.r
Level $342$
Weight $3$
Character orbit 342.r
Rep. character $\chi_{342}(125,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $4$
Sturm bound $180$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 342.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(180\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 256 32 224
Cusp forms 224 32 192
Eisenstein series 32 0 32

Trace form

\( 32 q + 32 q^{4} + O(q^{10}) \) \( 32 q + 32 q^{4} - 16 q^{13} - 64 q^{16} + 56 q^{19} - 16 q^{22} + 248 q^{25} - 112 q^{31} - 16 q^{34} + 240 q^{37} - 136 q^{43} + 320 q^{46} + 672 q^{49} + 32 q^{52} - 216 q^{55} - 192 q^{58} - 8 q^{61} - 256 q^{64} - 376 q^{67} - 144 q^{70} + 24 q^{73} - 64 q^{76} + 120 q^{79} + 176 q^{82} - 816 q^{85} - 64 q^{88} - 8 q^{91} - 64 q^{94} + 496 q^{97} + O(q^{100}) \)

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.r.a $4$ $9.319$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-52\) \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+6\beta _{1}q^{5}-13q^{7}+\cdots\)
342.3.r.b $4$ $9.319$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-28\) \(q-\beta _{1}q^{2}+2\beta _{2}q^{4}+3\beta _{1}q^{5}-7q^{7}+\cdots\)
342.3.r.c $12$ $9.319$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(20\) \(q+\beta _{5}q^{2}+(2+2\beta _{1})q^{4}+(-\beta _{3}-2\beta _{5}+\cdots)q^{5}+\cdots\)
342.3.r.d $12$ $9.319$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(60\) \(q-\beta _{5}q^{2}-2\beta _{2}q^{4}+(-\beta _{5}-\beta _{11})q^{5}+\cdots\)

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

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