# Properties

 Label 525.3.h Level $525$ Weight $3$ Character orbit 525.h Rep. character $\chi_{525}(76,\cdot)$ Character field $\Q$ Dimension $50$ Newform subspaces $5$ Sturm bound $240$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 525.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$240$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(525, [\chi])$$.

Total New Old
Modular forms 172 50 122
Cusp forms 148 50 98
Eisenstein series 24 0 24

## Trace form

 $$50 q + 2 q^{2} + 90 q^{4} + 6 q^{7} + 10 q^{8} - 150 q^{9} + O(q^{10})$$ $$50 q + 2 q^{2} + 90 q^{4} + 6 q^{7} + 10 q^{8} - 150 q^{9} + 12 q^{11} + 14 q^{14} + 106 q^{16} - 6 q^{18} - 30 q^{21} + 68 q^{22} + 92 q^{23} - 82 q^{28} - 20 q^{29} + 162 q^{32} - 270 q^{36} - 84 q^{37} - 60 q^{39} + 84 q^{42} - 204 q^{43} + 176 q^{44} - 376 q^{46} + 132 q^{49} - 48 q^{51} - 196 q^{53} + 358 q^{56} + 168 q^{57} + 476 q^{58} - 18 q^{63} + 662 q^{64} - 316 q^{67} + 228 q^{71} - 30 q^{72} + 256 q^{74} - 28 q^{77} - 432 q^{78} - 84 q^{79} + 450 q^{81} - 432 q^{84} - 1256 q^{86} + 676 q^{88} + 350 q^{91} - 276 q^{92} + 48 q^{93} - 790 q^{98} - 36 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(525, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
525.3.h.a $2$ $14.305$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$0$$ $$-2$$ $$q-q^{2}+\zeta_{6}q^{3}-3q^{4}-\zeta_{6}q^{6}+(-1+\cdots)q^{7}+\cdots$$
525.3.h.b $10$ $14.305$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$-2$$ $$0$$ $$0$$ $$-9$$ $$q-\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{1}-\beta _{3})q^{4}+\cdots$$
525.3.h.c $10$ $14.305$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$2$$ $$0$$ $$0$$ $$9$$ $$q+\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{1}-\beta _{3})q^{4}+\cdots$$
525.3.h.d $12$ $14.305$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$4$$ $$0$$ $$0$$ $$8$$ $$q+\beta _{5}q^{2}-\beta _{3}q^{3}+(4+\beta _{1})q^{4}-\beta _{9}q^{6}+\cdots$$
525.3.h.e $16$ $14.305$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}-\beta _{2}q^{3}+(2+\beta _{1})q^{4}+\beta _{4}q^{6}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(525, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(525, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 2}$$