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Properties

Label 342.4.s
Level $342$
Weight $4$
Character orbit 342.s
Rep. character $\chi_{342}(107,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $2$
Sturm bound $240$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(240\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(342, [\chi])\).

Total New Old
Modular forms 376 40 336
Cusp forms 344 40 304
Eisenstein series 32 0 32

Trace form

\( 40 q - 80 q^{4} - 56 q^{7} + O(q^{10}) \) \( 40 q - 80 q^{4} - 56 q^{7} + 156 q^{13} - 320 q^{16} - 88 q^{19} + 432 q^{22} + 764 q^{25} + 112 q^{28} + 720 q^{34} + 260 q^{43} + 2880 q^{49} - 624 q^{52} - 1320 q^{55} + 1536 q^{58} + 1324 q^{61} + 2560 q^{64} - 2172 q^{67} - 6192 q^{70} - 2572 q^{73} + 464 q^{76} + 3396 q^{79} + 2208 q^{82} - 1128 q^{85} + 3612 q^{91} - 7272 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(342, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
342.4.s.a 342.s 57.f $20$ $20.179$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-20\) \(0\) \(0\) \(-28\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+2\beta _{1})q^{2}-4\beta _{1}q^{4}+(\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
342.4.s.b 342.s 57.f $20$ $20.179$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(20\) \(0\) \(0\) \(-28\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-2\beta _{1})q^{2}-4\beta _{1}q^{4}+(-\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(342, [\chi]) \cong \)