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Properties

Label 378.2.t
Level $378$
Weight $2$
Character orbit 378.t
Rep. character $\chi_{378}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
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: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(378, [\chi])\).

Total New Old
Modular forms 168 16 152
Cusp forms 120 16 104
Eisenstein series 48 0 48

Trace form

\( 16 q + 8 q^{4} + 2 q^{7} + O(q^{10}) \) \( 16 q + 8 q^{4} + 2 q^{7} - 6 q^{13} + 6 q^{14} - 8 q^{16} - 18 q^{17} + 16 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{29} + 6 q^{31} + 30 q^{35} - 2 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} + 10 q^{49} + 12 q^{50} - 36 q^{53} - 12 q^{58} - 30 q^{59} - 60 q^{61} + 36 q^{62} - 16 q^{64} - 42 q^{65} + 14 q^{67} - 36 q^{68} + 18 q^{77} - 16 q^{79} - 12 q^{85} - 24 q^{89} - 12 q^{91} - 6 q^{92} + 66 q^{95} - 6 q^{97} - 24 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(378, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
378.2.t.a 378.t 63.s $16$ $3.018$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+(1-\beta _{8})q^{4}+(-\beta _{12}-\beta _{14}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(378, [\chi])\) into lower level spaces

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