Properties

Label 378.2.k
Level $378$
Weight $2$
Character orbit 378.k
Rep. character $\chi_{378}(215,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $4$
Sturm bound $144$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(10\)
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 20 148
Cusp forms 120 20 100
Eisenstein series 48 0 48

Trace form

\( 20 q + 10 q^{4} + 10 q^{7} + O(q^{10}) \) \( 20 q + 10 q^{4} + 10 q^{7} - 6 q^{10} - 10 q^{16} + 12 q^{19} + 12 q^{22} - 4 q^{25} + 8 q^{28} + 24 q^{31} + 14 q^{37} - 6 q^{40} + 44 q^{43} - 58 q^{49} - 18 q^{52} - 24 q^{58} - 30 q^{61} - 20 q^{64} - 26 q^{67} - 30 q^{70} - 120 q^{73} - 2 q^{79} - 24 q^{82} - 72 q^{85} + 6 q^{88} + 48 q^{91} + 120 q^{94} + O(q^{100}) \)

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.k.a $4$ $3.018$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-1+3\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
378.2.k.b $4$ $3.018$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2\zeta_{12}+4\zeta_{12}^{3})q^{5}+\cdots\)
378.2.k.c $4$ $3.018$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}-2\zeta_{12}^{3})q^{5}+\cdots\)
378.2.k.d $8$ $3.018$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-8\) \(q+\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(378, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)