Properties

Label 378.2.d
Level $378$
Weight $2$
Character orbit 378.d
Rep. character $\chi_{378}(377,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $3$
Sturm bound $144$
Trace bound $22$

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Defining parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(22\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

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

Total New Old
Modular forms 84 12 72
Cusp forms 60 12 48
Eisenstein series 24 0 24

Trace form

\( 12q - 12q^{4} + 6q^{7} + O(q^{10}) \) \( 12q - 12q^{4} + 6q^{7} + 12q^{16} + 12q^{25} - 6q^{28} + 12q^{37} - 60q^{43} + 30q^{49} - 36q^{58} - 12q^{64} - 12q^{67} - 18q^{70} + 24q^{79} + 72q^{85} - 36q^{91} + O(q^{100}) \)

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.d.a \(4\) \(3.018\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-10\) \(q-\zeta_{12}^{3}q^{2}-q^{4}+(-2\zeta_{12}+\zeta_{12}^{3})q^{5}+\cdots\)
378.2.d.b \(4\) \(3.018\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) \(q-\zeta_{12}q^{2}-q^{4}-\zeta_{12}^{3}q^{5}+(2-\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
378.2.d.c \(4\) \(3.018\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{12}q^{2}-q^{4}-2\zeta_{12}^{3}q^{5}+(2-\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(378, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)