Properties

Label 378.2.h
Level $378$
Weight $2$
Character orbit 378.h
Rep. character $\chi_{378}(289,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $4$
Sturm bound $144$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

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

\( 16q - 8q^{4} - 8q^{5} - 2q^{7} + O(q^{10}) \) \( 16q - 8q^{4} - 8q^{5} - 2q^{7} + 8q^{11} + 2q^{13} - 2q^{14} - 8q^{16} + 14q^{17} - 4q^{19} + 4q^{20} - 4q^{23} + 16q^{25} + 16q^{26} - 2q^{28} + 10q^{29} + 2q^{31} + 14q^{35} + 2q^{37} - 24q^{38} + 6q^{41} + 2q^{43} - 4q^{44} - 6q^{46} + 6q^{47} - 14q^{49} + 4q^{50} - 4q^{52} - 24q^{53} - 12q^{55} + 4q^{56} - 12q^{58} + 22q^{59} + 8q^{61} - 44q^{62} + 16q^{64} + 6q^{65} + 14q^{67} - 28q^{68} - 52q^{71} - 28q^{73} - 12q^{74} - 4q^{76} + 34q^{77} + 20q^{79} + 4q^{80} - 16q^{83} + 12q^{85} + 24q^{86} + 36q^{89} - 16q^{91} + 2q^{92} + 12q^{94} - 34q^{95} + 2q^{97} + 24q^{98} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
378.2.h.a \(2\) \(3.018\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-6\) \(5\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}+(3+\cdots)q^{7}+\cdots\)
378.2.h.b \(2\) \(3.018\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(6\) \(-1\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
378.2.h.c \(6\) \(3.018\) 6.0.309123.1 None \(-3\) \(0\) \(2\) \(-4\) \(q+(-1+\beta _{4})q^{2}-\beta _{4}q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
378.2.h.d \(6\) \(3.018\) 6.0.309123.1 None \(3\) \(0\) \(-10\) \(-2\) \(q+\beta _{4}q^{2}+(-1+\beta _{4})q^{4}+(-2-\beta _{1}+\cdots)q^{5}+\cdots\)

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

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