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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.4.e.a 63.e 7.c $2$ $3.717$ \(\Q(\sqrt{-3}) \) None \(-3\) \(0\) \(-3\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
63.4.e.b 63.e 7.c $2$ $3.717$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(7\) \(28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+4\zeta_{6}q^{4}+(7-7\zeta_{6})q^{5}+\cdots\)
63.4.e.c 63.e 7.c $6$ $3.717$ 6.0.9924270768.1 None \(1\) \(0\) \(11\) \(-13\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-8+\beta _{1}+\beta _{2}+8\beta _{4}+\beta _{5})q^{4}+\cdots\)
63.4.e.d 63.e 7.c $8$ $3.717$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{2}-\beta _{6})q^{4}+\cdots\)

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

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