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Properties

Label 378.3.bd
Level $378$
Weight $3$
Character orbit 378.bd
Rep. character $\chi_{378}(13,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $288$
Newform subspaces $1$
Sturm bound $216$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 378.bd (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(216\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(378, [\chi])\).

Total New Old
Modular forms 888 288 600
Cusp forms 840 288 552
Eisenstein series 48 0 48

Trace form

\( 288 q - 12 q^{9} + O(q^{10}) \) \( 288 q - 12 q^{9} + 36 q^{11} + 36 q^{14} - 24 q^{15} - 228 q^{21} + 288 q^{23} - 72 q^{29} - 288 q^{30} + 162 q^{35} + 96 q^{36} - 348 q^{39} - 48 q^{42} - 72 q^{49} - 144 q^{50} + 396 q^{51} + 1080 q^{53} + 72 q^{56} - 348 q^{57} + 72 q^{60} - 402 q^{63} - 1152 q^{64} + 180 q^{65} - 360 q^{70} + 216 q^{71} + 192 q^{72} - 432 q^{74} - 198 q^{77} - 96 q^{78} + 72 q^{79} + 324 q^{81} + 48 q^{84} - 360 q^{85} - 288 q^{86} - 198 q^{91} - 504 q^{92} - 336 q^{93} + 1008 q^{95} + 216 q^{98} - 936 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(378, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
378.3.bd.a 378.bd 189.y $288$ $10.300$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{3}^{\mathrm{old}}(378, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(378, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)