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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

\( 4 q + 2 q^{2} - 2 q^{5} - 6 q^{7} + 4 q^{10} - 2 q^{11} - 12 q^{13} - 2 q^{14} + 6 q^{19} + 8 q^{20} - 8 q^{22} + 6 q^{25} + 2 q^{26} + 16 q^{28} - 8 q^{29} - 2 q^{31} - 8 q^{32} + 2 q^{35} - 2 q^{37} + 2 q^{38}+ \cdots - 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.2.e.a 63.e 7.c $2$ $0.503$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 63.2.e.a \(0\) \(0\) \(0\) \(-1\) $\mathrm{U}(1)[D_{3}]$ \(q+2\zeta_{6}q^{4}+(1-3\zeta_{6})q^{7}-7q^{13}+(-4+\cdots)q^{16}+\cdots\)
63.2.e.b 63.e 7.c $2$ $0.503$ \(\Q(\sqrt{-3}) \) None 21.2.e.a \(2\) \(0\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots\)

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

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