↑

Properties

Label 378.3.i
Level $378$
Weight $3$
Character orbit 378.i
Rep. character $\chi_{378}(179,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $1$
Sturm bound $216$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 378.i (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

\( 32 q + 32 q^{4} + 2 q^{7} + O(q^{10}) \) \( 32 q + 32 q^{4} + 2 q^{7} + 10 q^{13} - 36 q^{14} - 64 q^{16} - 54 q^{17} + 28 q^{19} - 160 q^{25} - 72 q^{26} - 4 q^{28} - 36 q^{29} - 8 q^{31} - 90 q^{35} + 22 q^{37} - 72 q^{41} + 16 q^{43} + 72 q^{44} - 12 q^{46} + 108 q^{47} + 74 q^{49} + 288 q^{50} + 40 q^{52} - 72 q^{53} - 24 q^{55} + 48 q^{58} + 90 q^{59} - 62 q^{61} - 256 q^{64} - 378 q^{65} + 70 q^{67} - 108 q^{70} + 196 q^{73} - 56 q^{76} - 630 q^{77} - 38 q^{79} + 60 q^{85} - 486 q^{89} - 122 q^{91} - 252 q^{92} + 168 q^{94} + 72 q^{95} - 38 q^{97} + 288 q^{98} + O(q^{100}) \)

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

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

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