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Properties

Label 378.2.ba
Level $378$
Weight $2$
Character orbit 378.ba
Rep. character $\chi_{378}(47,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $144$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.ba (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(378, [\chi])\).

Total New Old
Modular forms 456 144 312
Cusp forms 408 144 264
Eisenstein series 48 0 48

Trace form

\( 144 q - 18 q^{6} + 24 q^{9} + O(q^{10}) \) \( 144 q - 18 q^{6} + 24 q^{9} - 24 q^{11} + 6 q^{14} + 12 q^{15} - 30 q^{21} - 42 q^{23} - 6 q^{29} - 18 q^{30} + 6 q^{36} + 48 q^{39} - 48 q^{42} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 12 q^{50} - 36 q^{51} - 90 q^{53} + 6 q^{56} - 6 q^{57} + 18 q^{60} + 54 q^{61} - 24 q^{63} + 72 q^{64} + 78 q^{65} - 72 q^{66} - 54 q^{68} + 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} - 36 q^{74} - 6 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 36 q^{91} - 42 q^{92} + 96 q^{93} - 66 q^{95} - 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(378, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
378.2.ba.a 378.ba 189.ad $144$ $3.018$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(378, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(378, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)