# Properties

 Label 275.6.b Level $275$ Weight $6$ Character orbit 275.b Rep. character $\chi_{275}(199,\cdot)$ Character field $\Q$ Dimension $76$ Newform subspaces $8$ Sturm bound $180$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$275 = 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 275.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$180$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(275, [\chi])$$.

Total New Old
Modular forms 156 76 80
Cusp forms 144 76 68
Eisenstein series 12 0 12

## Trace form

 $$76 q - 1208 q^{4} + 520 q^{6} - 7302 q^{9} + O(q^{10})$$ $$76 q - 1208 q^{4} + 520 q^{6} - 7302 q^{9} + 484 q^{11} + 2260 q^{14} + 18032 q^{16} - 5940 q^{19} - 15248 q^{21} + 8012 q^{24} + 23624 q^{26} - 22064 q^{29} + 14998 q^{31} + 75040 q^{34} + 112968 q^{36} + 30924 q^{39} - 62176 q^{41} - 14520 q^{44} - 53280 q^{46} - 214944 q^{49} - 57716 q^{51} - 52412 q^{54} - 86916 q^{56} - 98762 q^{59} - 170820 q^{61} - 554116 q^{64} + 34848 q^{66} + 57146 q^{69} + 313850 q^{71} + 148044 q^{74} + 96420 q^{76} + 23936 q^{79} + 183676 q^{81} + 1133644 q^{84} - 382700 q^{86} + 93614 q^{89} + 78476 q^{91} - 105992 q^{94} - 19584 q^{96} - 2662 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(275, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
275.6.b.a $2$ $44.106$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+4iq^{2}-15iq^{3}+2^{4}q^{4}+60q^{6}+\cdots$$
275.6.b.b $6$ $44.106$ 6.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}+(6\beta _{3}-\beta _{4}+\beta _{5})q^{3}+(-30+\cdots)q^{4}+\cdots$$
275.6.b.c $6$ $44.106$ 6.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(-\beta _{1}-2\beta _{3})q^{3}+(-14+\cdots)q^{4}+\cdots$$
275.6.b.d $8$ $44.106$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{6})q^{3}+(-15+\beta _{3}+\cdots)q^{4}+\cdots$$
275.6.b.e $10$ $44.106$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+(\beta _{4}+\beta _{7})q^{3}+(-23+\beta _{1}+\cdots)q^{4}+\cdots$$
275.6.b.f $12$ $44.106$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{9})q^{3}+(-19+\beta _{2}+\cdots)q^{4}+\cdots$$
275.6.b.g $16$ $44.106$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{9})q^{3}+(-14+\beta _{2}+\cdots)q^{4}+\cdots$$
275.6.b.h $16$ $44.106$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{8}q^{2}+(\beta _{9}-\beta _{11})q^{3}+(-11+\beta _{1}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(275, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(275, [\chi]) \simeq$$ $$S_{6}^{\mathrm{new}}(5, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 2}$$