# Properties

 Label 975.2.w Level $975$ Weight $2$ Character orbit 975.w Rep. character $\chi_{975}(49,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $80$ Newform subspaces $11$ Sturm bound $280$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$975 = 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 975.w (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$11$$ Sturm bound: $$280$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$2$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(975, [\chi])$$.

Total New Old
Modular forms 304 80 224
Cusp forms 256 80 176
Eisenstein series 48 0 48

## Trace form

 $$80q - 36q^{4} + 40q^{9} + O(q^{10})$$ $$80q - 36q^{4} + 40q^{9} + 24q^{11} - 16q^{14} - 20q^{16} + 30q^{19} - 32q^{26} + 4q^{29} + 36q^{36} + 10q^{39} - 24q^{41} + 36q^{46} - 42q^{49} + 48q^{51} + 76q^{56} - 132q^{59} + 24q^{61} - 56q^{64} + 28q^{69} - 24q^{71} - 32q^{74} - 156q^{76} + 64q^{79} - 40q^{81} - 24q^{84} + 96q^{89} - 86q^{91} + 24q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(975, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
975.2.w.a $$4$$ $$7.785$$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$0$$ $$-2$$ $$q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$$
975.2.w.b $$4$$ $$7.785$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$$
975.2.w.c $$4$$ $$7.785$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$$
975.2.w.d $$4$$ $$7.785$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{3}+2\zeta_{12}^{2}q^{4}+(-\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots$$
975.2.w.e $$4$$ $$7.785$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}+2\zeta_{12}^{2}q^{4}+(2\zeta_{12}+2\zeta_{12}^{3})q^{7}+\cdots$$
975.2.w.f $$4$$ $$7.785$$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$0$$ $$2$$ $$q+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$$
975.2.w.g $$8$$ $$7.785$$ 8.0.56070144.2 None $$-2$$ $$0$$ $$0$$ $$6$$ $$q+(-\beta _{3}+\beta _{6}-\beta _{7})q^{2}-\beta _{4}q^{3}+(-1+\cdots)q^{4}+\cdots$$
975.2.w.h $$8$$ $$7.785$$ 8.0.191102976.5 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{5}+\beta _{7})q^{2}+\beta _{6}q^{3}+(-1+\cdots)q^{4}+\cdots$$
975.2.w.i $$8$$ $$7.785$$ 8.0.191102976.5 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{5}+\beta _{7})q^{2}-\beta _{6}q^{3}+(-1+\cdots)q^{4}+\cdots$$
975.2.w.j $$8$$ $$7.785$$ 8.0.56070144.2 None $$2$$ $$0$$ $$0$$ $$-6$$ $$q+(\beta _{3}-\beta _{6}+\beta _{7})q^{2}+\beta _{4}q^{3}+(-1+\cdots)q^{4}+\cdots$$
975.2.w.k $$24$$ $$7.785$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(975, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(975, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(325, [\chi])$$$$^{\oplus 2}$$