Properties

Label 63.4.e
Level $63$
Weight $4$
Character orbit 63.e
Rep. character $\chi_{63}(37,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $18$
Newform subspaces $4$
Sturm bound $32$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(32\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(63, [\chi])\).

Total New Old
Modular forms 56 22 34
Cusp forms 40 18 22
Eisenstein series 16 4 12

Trace form

\( 18q - 28q^{4} + 15q^{5} - 4q^{7} - 72q^{8} + O(q^{10}) \) \( 18q - 28q^{4} + 15q^{5} - 4q^{7} - 72q^{8} + 10q^{10} + 15q^{11} + 172q^{13} + 228q^{14} - 52q^{16} + 111q^{17} - 53q^{19} - 816q^{20} - 116q^{22} - 27q^{23} - 304q^{25} + 438q^{26} - 192q^{28} + 372q^{29} - 19q^{31} + 888q^{32} + 1404q^{34} - 189q^{35} + 209q^{37} - 252q^{38} - 612q^{40} - 1908q^{41} - 1152q^{43} - 900q^{44} - 594q^{46} + 285q^{47} - 462q^{49} + 2364q^{50} - 276q^{52} + 1059q^{53} + 2978q^{55} - 480q^{56} + 1936q^{58} + 1023q^{59} - 731q^{61} - 4224q^{62} - 408q^{64} - 378q^{65} - 1307q^{67} + 2112q^{68} + 2210q^{70} + 912q^{71} - 1987q^{73} + 2388q^{74} - 192q^{76} - 723q^{77} - 1233q^{79} + 276q^{80} - 2224q^{82} - 4176q^{83} + 570q^{85} - 3534q^{86} - 1596q^{88} + 2343q^{89} - 132q^{91} + 240q^{92} + 3570q^{94} - 345q^{95} + 5300q^{97} + 4806q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
63.4.e.a \(2\) \(3.717\) \(\Q(\sqrt{-3}) \) None \(-3\) \(0\) \(-3\) \(-7\) \(q+(-3+3\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
63.4.e.b \(2\) \(3.717\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(7\) \(28\) \(q+(2-2\zeta_{6})q^{2}+4\zeta_{6}q^{4}+(7-7\zeta_{6})q^{5}+\cdots\)
63.4.e.c \(6\) \(3.717\) 6.0.9924270768.1 None \(1\) \(0\) \(11\) \(-13\) \(q+\beta _{1}q^{2}+(-8+\beta _{1}+\beta _{2}+8\beta _{4}+\beta _{5})q^{4}+\cdots\)
63.4.e.d \(8\) \(3.717\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(-12\) \(q+(\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{2}-\beta _{6})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)