Properties

Label 378.3.j
Level $378$
Weight $3$
Character orbit 378.j
Rep. character $\chi_{378}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
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 312 32 280
Cusp forms 264 32 232
Eisenstein series 48 0 48

Trace form

\( 32 q - 32 q^{4} - 2 q^{7} + O(q^{10}) \) \( 32 q - 32 q^{4} - 2 q^{7} - 24 q^{11} - 30 q^{13} + 12 q^{14} - 64 q^{16} - 54 q^{17} - 84 q^{23} - 160 q^{25} + 72 q^{26} - 4 q^{28} + 84 q^{29} - 24 q^{31} + 66 q^{35} - 22 q^{37} - 396 q^{41} - 16 q^{43} + 24 q^{44} + 12 q^{46} - 108 q^{47} - 22 q^{49} + 96 q^{50} + 252 q^{53} - 48 q^{56} + 48 q^{58} + 90 q^{59} - 102 q^{61} + 256 q^{64} + 6 q^{65} + 70 q^{67} - 108 q^{70} - 300 q^{71} - 144 q^{74} + 114 q^{77} + 106 q^{79} + 756 q^{83} - 60 q^{85} - 240 q^{86} - 414 q^{89} - 186 q^{91} + 84 q^{92} + 552 q^{95} + 114 q^{97} + 96 q^{98} + O(q^{100}) \)

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.j.a 378.j 63.k $32$ $10.300$ None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{3}^{\mathrm{old}}(378, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)