# Properties

 Label 175.8.b Level $175$ Weight $8$ Character orbit 175.b Rep. character $\chi_{175}(99,\cdot)$ Character field $\Q$ Dimension $62$ Newform subspaces $8$ Sturm bound $160$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$8$$ Character orbit: $$[\chi]$$ $$=$$ 175.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$160$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(175, [\chi])$$.

Total New Old
Modular forms 146 62 84
Cusp forms 134 62 72
Eisenstein series 12 0 12

## Trace form

 $$62 q - 3736 q^{4} - 216 q^{6} - 39114 q^{9} + O(q^{10})$$ $$62 q - 3736 q^{4} - 216 q^{6} - 39114 q^{9} - 16556 q^{11} + 10976 q^{14} + 241032 q^{16} + 92840 q^{19} + 19208 q^{21} - 595700 q^{24} + 214284 q^{26} - 371140 q^{29} + 1079644 q^{31} + 224888 q^{34} + 1507812 q^{36} + 2427052 q^{39} - 1649656 q^{41} - 475242 q^{44} - 7705286 q^{46} - 7294238 q^{49} - 1478836 q^{51} - 11167580 q^{54} - 956970 q^{56} - 8268340 q^{59} + 2621904 q^{61} - 25530846 q^{64} + 45621428 q^{66} + 11264892 q^{69} - 4023656 q^{71} + 23927058 q^{74} - 9332740 q^{76} - 2383980 q^{79} + 23252662 q^{81} - 7288064 q^{84} - 48314346 q^{86} - 24913680 q^{89} - 14503412 q^{91} + 97282468 q^{94} + 106266924 q^{96} - 31535248 q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(175, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.8.b.a $2$ $54.667$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+6iq^{2}-42iq^{3}+92q^{4}+252q^{6}+\cdots$$
175.8.b.b $4$ $54.667$ $$\Q(i, \sqrt{865})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{2})q^{2}+(2\beta _{1}-46\beta _{2})q^{3}+(-92+\cdots)q^{4}+\cdots$$
175.8.b.c $4$ $54.667$ $$\Q(i, \sqrt{11})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(8\beta _{1}+\beta _{3})q^{2}+(15\beta _{1}+6\beta _{3})q^{3}+\cdots$$
175.8.b.d $6$ $54.667$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+8\beta _{2})q^{2}+(-2\beta _{1}-17\beta _{2}-\beta _{5})q^{3}+\cdots$$
175.8.b.e $8$ $54.667$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}-\beta _{4})q^{2}+(9\beta _{2}+\beta _{4}+2\beta _{5}+\cdots)q^{3}+\cdots$$
175.8.b.f $10$ $54.667$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-2\beta _{5})q^{2}+(13\beta _{5}-\beta _{7})q^{3}+(-111+\cdots)q^{4}+\cdots$$
175.8.b.g $12$ $54.667$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{7})q^{2}+(\beta _{1}+5\beta _{7}+\beta _{8})q^{3}+\cdots$$
175.8.b.h $16$ $54.667$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+2\beta _{9})q^{2}+(-7\beta _{9}-\beta _{10})q^{3}+\cdots$$

## Decomposition of $$S_{8}^{\mathrm{old}}(175, [\chi])$$ into lower level spaces

$$S_{8}^{\mathrm{old}}(175, [\chi]) \simeq$$ $$S_{8}^{\mathrm{new}}(5, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$