Properties

 Label 78.4.g Level $78$ Weight $4$ Character orbit 78.g Rep. character $\chi_{78}(5,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $28$ Newform subspaces $1$ Sturm bound $56$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$78 = 2 \cdot 3 \cdot 13$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 78.g (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$39$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$56$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(78, [\chi])$$.

Total New Old
Modular forms 92 28 64
Cusp forms 76 28 48
Eisenstein series 16 0 16

Trace form

 $$28 q + 20 q^{7} + O(q^{10})$$ $$28 q + 20 q^{7} + 120 q^{13} + 168 q^{15} - 448 q^{16} - 96 q^{18} - 124 q^{19} + 264 q^{21} + 900 q^{27} - 80 q^{28} + 364 q^{31} - 1188 q^{33} - 672 q^{34} + 796 q^{37} - 912 q^{39} - 360 q^{42} - 252 q^{45} + 384 q^{46} + 592 q^{52} - 72 q^{54} + 144 q^{55} - 540 q^{57} + 1056 q^{58} + 672 q^{60} - 816 q^{61} + 252 q^{63} + 3072 q^{66} - 124 q^{67} + 192 q^{70} - 384 q^{72} + 1028 q^{73} - 496 q^{76} + 984 q^{78} - 10632 q^{79} - 3888 q^{81} - 1056 q^{84} + 9288 q^{85} + 1632 q^{87} - 844 q^{91} + 1788 q^{93} + 5232 q^{94} + 6628 q^{97} - 2052 q^{99} + O(q^{100})$$

Decomposition of $$S_{4}^{\mathrm{new}}(78, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
78.4.g.a $28$ $4.602$ None $$0$$ $$0$$ $$0$$ $$20$$

Decomposition of $$S_{4}^{\mathrm{old}}(78, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(78, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 2}$$