# 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

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

## 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

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