Properties

Label 63.2.e
Level 63
Weight 2
Character orbit e
Rep. character \(\chi_{63}(37,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 4
Newforms 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: \(\Q(\zeta_{3})\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(63, [\chi])\) into irreducible Hecke orbits

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

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