# Properties

 Label 6.7.b Level $6$ Weight $7$ Character orbit 6.b Rep. character $\chi_{6}(5,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $7$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$6 = 2 \cdot 3$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 6.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$7$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(6, [\chi])$$.

Total New Old
Modular forms 8 2 6
Cusp forms 4 2 2
Eisenstein series 4 0 4

## Trace form

 $$2 q + 42 q^{3} - 64 q^{4} - 192 q^{6} + 4 q^{7} + 306 q^{9} + O(q^{10})$$ $$2 q + 42 q^{3} - 64 q^{4} - 192 q^{6} + 4 q^{7} + 306 q^{9} + 1920 q^{10} - 1344 q^{12} - 5900 q^{13} + 5760 q^{15} + 2048 q^{16} - 8064 q^{18} + 10516 q^{19} + 84 q^{21} + 384 q^{22} + 6144 q^{24} - 26350 q^{25} - 17766 q^{27} - 128 q^{28} + 40320 q^{30} + 45796 q^{31} + 1152 q^{33} - 50688 q^{34} - 9792 q^{36} + 68116 q^{37} - 123900 q^{39} - 61440 q^{40} - 384 q^{42} - 12812 q^{43} + 241920 q^{45} + 115968 q^{46} + 43008 q^{48} - 235290 q^{49} - 152064 q^{51} + 188800 q^{52} - 198720 q^{54} - 11520 q^{55} + 220836 q^{57} - 24960 q^{58} - 184320 q^{60} - 125132 q^{61} + 612 q^{63} - 65536 q^{64} + 8064 q^{66} + 877396 q^{67} + 347904 q^{69} + 3840 q^{70} + 258048 q^{72} - 1461020 q^{73} - 553350 q^{75} - 336512 q^{76} + 566400 q^{78} + 681124 q^{79} - 969246 q^{81} + 189696 q^{82} - 2688 q^{84} + 1520640 q^{85} - 74880 q^{87} - 12288 q^{88} + 293760 q^{90} - 11800 q^{91} + 961716 q^{93} - 2035200 q^{94} - 196608 q^{96} - 562172 q^{97} + 48384 q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(6, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
6.7.b.a $2$ $1.380$ $$\Q(\sqrt{-2})$$ None $$0$$ $$42$$ $$0$$ $$4$$ $$q+\beta q^{2}+(21+3\beta )q^{3}-2^{5}q^{4}-30\beta q^{5}+\cdots$$

## Decomposition of $$S_{7}^{\mathrm{old}}(6, [\chi])$$ into lower level spaces

$$S_{7}^{\mathrm{old}}(6, [\chi]) \cong$$ $$S_{7}^{\mathrm{new}}(3, [\chi])$$$$^{\oplus 2}$$