↑

Properties

Label 378.4.t
Level $378$
Weight $4$
Character orbit 378.t
Rep. character $\chi_{378}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 378.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(378, [\chi])\).

Total New Old
Modular forms 456 48 408
Cusp forms 408 48 360
Eisenstein series 48 0 48

Trace form

\( 48 q + 96 q^{4} - 12 q^{7} + O(q^{10}) \) \( 48 q + 96 q^{4} - 12 q^{7} - 72 q^{13} + 132 q^{14} - 384 q^{16} + 144 q^{17} + 1200 q^{25} + 120 q^{26} + 48 q^{28} - 42 q^{29} - 90 q^{31} - 780 q^{35} - 168 q^{37} - 618 q^{41} - 42 q^{43} + 96 q^{44} - 252 q^{46} - 198 q^{47} - 636 q^{49} - 1464 q^{50} - 36 q^{53} + 504 q^{58} + 1500 q^{59} + 2466 q^{61} + 2952 q^{62} - 3072 q^{64} + 84 q^{65} - 588 q^{67} + 1152 q^{68} + 216 q^{70} - 1548 q^{77} + 1230 q^{79} + 720 q^{85} - 4398 q^{89} - 90 q^{91} + 1632 q^{92} - 3246 q^{95} - 1584 q^{97} - 1104 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(378, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
378.4.t.a 378.t 63.s $48$ $22.303$ None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(378, [\chi])\) into lower level spaces

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