Properties

Label 63.2.e
Level $63$
Weight $2$
Character orbit 63.e
Rep. character $\chi_{63}(37,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $4$
Newform subspaces $2$
Sturm bound $16$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 63.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(63, [\chi])\).

Total New Old
Modular forms 24 8 16
Cusp forms 8 4 4
Eisenstein series 16 4 12

Trace form

\( 4q + 2q^{2} - 2q^{5} - 6q^{7} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{5} - 6q^{7} + 4q^{10} - 2q^{11} - 12q^{13} - 2q^{14} + 6q^{19} + 8q^{20} - 8q^{22} + 6q^{25} + 2q^{26} + 16q^{28} - 8q^{29} - 2q^{31} - 8q^{32} + 2q^{35} - 2q^{37} + 2q^{38} + 20q^{41} + 20q^{43} - 4q^{44} - 6q^{47} - 2q^{49} + 4q^{50} - 16q^{52} + 12q^{53} + 8q^{55} - 8q^{58} - 12q^{59} - 24q^{61} - 36q^{62} - 32q^{64} - 2q^{65} - 6q^{67} - 16q^{70} + 12q^{71} + 10q^{73} + 6q^{74} + 32q^{76} + 8q^{77} + 14q^{79} + 8q^{80} + 20q^{82} - 12q^{83} + 10q^{86} + 16q^{89} + 2q^{91} + 12q^{94} - 2q^{95} + 16q^{97} - 4q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
63.2.e.a \(2\) \(0.503\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) \(q+2\zeta_{6}q^{4}+(1-3\zeta_{6})q^{7}-7q^{13}+(-4+\cdots)q^{16}+\cdots\)
63.2.e.b \(2\) \(0.503\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-2\) \(-5\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)