# Properties

 Label 275.4.b Level $275$ Weight $4$ Character orbit 275.b Rep. character $\chi_{275}(199,\cdot)$ Character field $\Q$ Dimension $44$ Newform subspaces $7$ Sturm bound $120$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$275 = 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 275.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$120$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(275, [\chi])$$.

Total New Old
Modular forms 96 44 52
Cusp forms 84 44 40
Eisenstein series 12 0 12

## Trace form

 $$44q - 192q^{4} - 8q^{6} - 336q^{9} + O(q^{10})$$ $$44q - 192q^{4} - 8q^{6} - 336q^{9} - 44q^{11} + 52q^{14} + 592q^{16} + 24q^{19} + 64q^{21} + 428q^{24} - 568q^{26} - 320q^{29} - 688q^{31} - 104q^{34} + 1344q^{36} - 1752q^{39} + 680q^{41} + 1056q^{44} - 912q^{46} - 2588q^{49} - 800q^{51} + 3076q^{54} - 3588q^{56} + 124q^{59} + 4600q^{61} - 964q^{64} - 528q^{66} + 6716q^{69} - 184q^{71} - 9180q^{74} - 6364q^{76} + 2864q^{79} + 5116q^{81} - 5684q^{84} + 6172q^{86} - 3136q^{89} - 2072q^{91} + 6952q^{94} + 2592q^{96} + 968q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(275, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
275.4.b.a $$2$$ $$16.226$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+3iq^{3}+7q^{4}-3q^{6}-9iq^{7}+\cdots$$
275.4.b.b $$4$$ $$16.226$$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+2\beta _{2})q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(-5+\cdots)q^{4}+\cdots$$
275.4.b.c $$4$$ $$16.226$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}-4\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
275.4.b.d $$6$$ $$16.226$$ 6.0.5161984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{3}+\beta _{4}-\beta _{5})q^{2}+(-\beta _{3}-3\beta _{4}+\cdots)q^{3}+\cdots$$
275.4.b.e $$8$$ $$16.226$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(-5+\beta _{2}+\cdots)q^{4}+\cdots$$
275.4.b.f $$10$$ $$16.226$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{8})q^{3}+(-8+\beta _{2}+\cdots)q^{4}+\cdots$$
275.4.b.g $$10$$ $$16.226$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-2+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(275, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(275, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 2}$$