# Properties

 Label 20.7.b Level $20$ Weight $7$ Character orbit 20.b Rep. character $\chi_{20}(11,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $1$ Sturm bound $21$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$20 = 2^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 20.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$21$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(20, [\chi])$$.

Total New Old
Modular forms 20 12 8
Cusp forms 16 12 4
Eisenstein series 4 0 4

## Trace form

 $$12q - 10q^{2} + 156q^{4} - 672q^{6} + 440q^{8} - 1996q^{9} + O(q^{10})$$ $$12q - 10q^{2} + 156q^{4} - 672q^{6} + 440q^{8} - 1996q^{9} + 750q^{10} - 440q^{12} - 5040q^{13} + 6248q^{14} + 3312q^{16} + 6840q^{17} + 15790q^{18} - 3500q^{20} - 27464q^{21} - 26160q^{22} + 28528q^{24} + 37500q^{25} - 18684q^{26} + 19320q^{28} - 74968q^{29} - 13000q^{30} - 60800q^{32} + 112880q^{33} + 48204q^{34} - 128580q^{36} + 62640q^{37} + 74800q^{38} + 57000q^{40} - 16976q^{41} - 138360q^{42} - 222160q^{44} + 77000q^{45} - 144792q^{46} + 297600q^{48} + 72564q^{49} - 31250q^{50} + 548280q^{52} + 322160q^{53} + 150416q^{54} - 246512q^{56} - 1213440q^{57} + 350700q^{58} + 157000q^{60} + 46464q^{61} - 7120q^{62} - 542784q^{64} - 133000q^{65} - 65200q^{66} - 1678280q^{68} + 41256q^{69} - 360000q^{70} + 2317560q^{72} - 415080q^{73} + 1581924q^{74} + 208320q^{76} + 75600q^{77} + 473200q^{78} + 734000q^{80} + 2287428q^{81} - 3169500q^{82} - 2256224q^{84} + 372000q^{85} - 62512q^{86} - 278880q^{88} + 278392q^{89} - 2162250q^{90} + 4095720q^{92} - 3646000q^{93} + 4706568q^{94} - 2641152q^{96} + 2344680q^{97} + 1050270q^{98} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(20, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
20.7.b.a $$12$$ $$4.601$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-10$$ $$0$$ $$0$$ $$0$$ $$q+(-1-\beta _{2})q^{2}+(-\beta _{2}-\beta _{6})q^{3}+(13+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{7}^{\mathrm{old}}(20, [\chi])$$ into lower level spaces

$$S_{7}^{\mathrm{old}}(20, [\chi]) \cong$$ $$S_{7}^{\mathrm{new}}(4, [\chi])$$$$^{\oplus 2}$$