Properties

Label 342.2.bf
Level $342$
Weight $2$
Character orbit 342.bf
Rep. character $\chi_{342}(155,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $120$
Newform subspaces $3$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 342.bf (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 384 120 264
Cusp forms 336 120 216
Eisenstein series 48 0 48

Trace form

\( 120 q + 3 q^{3} + 3 q^{6} - 3 q^{9} + O(q^{10}) \) \( 120 q + 3 q^{3} + 3 q^{6} - 3 q^{9} + 6 q^{13} - 6 q^{15} + 54 q^{17} + 36 q^{18} + 6 q^{19} - 9 q^{22} - 6 q^{24} - 9 q^{27} + 6 q^{28} - 54 q^{29} + 3 q^{33} - 3 q^{36} + 9 q^{38} - 6 q^{39} + 9 q^{41} + 12 q^{43} - 3 q^{48} + 120 q^{49} - 72 q^{50} - 72 q^{51} - 6 q^{52} - 120 q^{57} - 153 q^{59} + 6 q^{60} - 84 q^{61} - 60 q^{63} - 60 q^{64} + 66 q^{66} - 51 q^{67} - 54 q^{69} - 3 q^{72} - 24 q^{73} - 42 q^{78} + 6 q^{79} + 69 q^{81} - 9 q^{82} - 36 q^{87} + 54 q^{89} + 6 q^{90} - 12 q^{91} - 36 q^{92} + 48 q^{93} - 9 q^{97} - 108 q^{98} - 51 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
342.2.bf.a 342.bf 171.ad $12$ $2.731$ 12.0.\(\cdots\).1 None \(0\) \(-6\) \(0\) \(18\) $\mathrm{SU}(2)[C_{18}]$ \(q+(\beta _{6}-\beta _{10})q^{2}+(-1+\beta _{8})q^{3}-\beta _{7}q^{4}+\cdots\)
342.2.bf.b 342.bf 171.ad $48$ $2.731$ None \(0\) \(9\) \(0\) \(-18\) $\mathrm{SU}(2)[C_{18}]$
342.2.bf.c 342.bf 171.ad $60$ $2.731$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

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

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