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

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

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

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