# Properties

 Label 25.9.c Level $25$ Weight $9$ Character orbit 25.c Rep. character $\chi_{25}(7,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $22$ Newform subspaces $3$ Sturm bound $22$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$25 = 5^{2}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 25.c (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$22$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(25, [\chi])$$.

Total New Old
Modular forms 46 26 20
Cusp forms 34 22 12
Eisenstein series 12 4 8

## Trace form

 $$22q + 2q^{2} + 72q^{3} - 3516q^{6} + 2352q^{7} + 8220q^{8} + O(q^{10})$$ $$22q + 2q^{2} + 72q^{3} - 3516q^{6} + 2352q^{7} + 8220q^{8} - 46396q^{11} + 45912q^{12} + 119142q^{13} - 699388q^{16} + 265502q^{17} + 454062q^{18} - 873216q^{21} + 35664q^{22} - 28888q^{23} + 4344524q^{26} - 392040q^{27} - 1305192q^{28} - 1695176q^{31} - 3033928q^{32} - 4269096q^{33} + 9851772q^{36} + 454002q^{37} - 1443720q^{38} + 8145284q^{41} - 4223856q^{42} - 792648q^{43} - 33395736q^{46} + 15313352q^{47} + 21677712q^{48} - 19367916q^{51} + 735732q^{52} + 13509122q^{53} - 23241360q^{56} + 34625520q^{57} + 23903520q^{58} - 57062296q^{61} - 53913416q^{62} - 44837688q^{63} + 223372788q^{66} + 32827752q^{67} - 8118692q^{68} - 154125736q^{71} - 82596420q^{72} - 111859638q^{73} + 358863380q^{76} - 26260136q^{77} - 31125576q^{78} - 81460278q^{81} - 38023056q^{82} + 14768432q^{83} + 23310944q^{86} + 133207680q^{87} + 44555040q^{88} + 50148624q^{91} - 69931048q^{92} + 96798024q^{93} - 1381059876q^{96} + 186656202q^{97} + 345959698q^{98} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(25, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
25.9.c.a $$4$$ $$10.184$$ $$\Q(i, \sqrt{141})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+\beta _{2}q^{3}-26\beta _{1}q^{4}+282q^{6}+\cdots$$
25.9.c.b $$6$$ $$10.184$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$2$$ $$72$$ $$0$$ $$2352$$ $$q+\beta _{3}q^{2}+(12+12\beta _{1}+\beta _{2}+\beta _{5})q^{3}+\cdots$$
25.9.c.c $$12$$ $$10.184$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(-\beta _{5}-\beta _{6}-\beta _{7})q^{3}+(281\beta _{1}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{9}^{\mathrm{old}}(25, [\chi])$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(25, [\chi]) \cong$$ $$S_{9}^{\mathrm{new}}(5, [\chi])$$$$^{\oplus 2}$$