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Properties

Label 378.3.bb
Level $378$
Weight $3$
Character orbit 378.bb
Rep. character $\chi_{378}(29,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $216$
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.bb (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
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 888 216 672
Cusp forms 840 216 624
Eisenstein series 48 0 48

Trace form

\( 216 q - 36 q^{5} + 12 q^{9} + O(q^{10}) \) \( 216 q - 36 q^{5} + 12 q^{9} + 24 q^{12} + 60 q^{15} + 96 q^{18} + 144 q^{20} - 72 q^{22} + 72 q^{23} - 36 q^{25} - 108 q^{27} - 216 q^{29} + 180 q^{31} - 144 q^{33} + 144 q^{34} - 240 q^{36} - 360 q^{38} + 48 q^{39} - 108 q^{41} - 180 q^{43} + 636 q^{45} + 324 q^{47} + 48 q^{48} - 144 q^{50} + 504 q^{51} + 360 q^{54} - 492 q^{57} - 324 q^{59} + 864 q^{64} - 576 q^{65} + 1188 q^{67} + 144 q^{68} + 1056 q^{69} + 648 q^{71} + 192 q^{72} + 576 q^{74} + 600 q^{75} + 144 q^{76} + 288 q^{78} + 72 q^{79} - 564 q^{81} - 1188 q^{83} - 168 q^{84} - 360 q^{85} - 792 q^{86} - 120 q^{87} - 288 q^{88} - 1296 q^{89} - 1440 q^{90} - 288 q^{92} - 588 q^{93} - 1224 q^{95} - 192 q^{96} - 1404 q^{97} - 468 q^{99} + O(q^{100}) \)

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.bb.a 378.bb 27.f $216$ $10.300$ None \(0\) \(0\) \(-36\) \(0\) $\mathrm{SU}(2)[C_{18}]$

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

\( S_{3}^{\mathrm{old}}(378, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)