# Properties

 Label 300.3.c Level $300$ Weight $3$ Character orbit 300.c Rep. character $\chi_{300}(151,\cdot)$ Character field $\Q$ Dimension $38$ Newform subspaces $7$ Sturm bound $180$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$300 = 2^{2} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 300.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$4$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$180$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$7$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(300, [\chi])$$.

Total New Old
Modular forms 132 38 94
Cusp forms 108 38 70
Eisenstein series 24 0 24

## Trace form

 $$38q - 2q^{2} - 8q^{4} - 6q^{6} + 4q^{8} - 114q^{9} + O(q^{10})$$ $$38q - 2q^{2} - 8q^{4} - 6q^{6} + 4q^{8} - 114q^{9} + 12q^{12} - 20q^{13} + 52q^{14} + 20q^{16} - 20q^{17} + 6q^{18} + 24q^{21} - 92q^{22} - 36q^{24} - 16q^{26} - 76q^{28} - 12q^{29} + 108q^{32} + 24q^{33} + 164q^{34} + 24q^{36} + 60q^{37} - 32q^{38} - 116q^{41} - 84q^{42} + 64q^{46} - 96q^{48} - 234q^{49} + 136q^{52} - 204q^{53} + 18q^{54} - 472q^{56} - 72q^{57} + 152q^{58} + 156q^{61} + 32q^{62} + 316q^{64} - 168q^{66} + 224q^{68} - 96q^{69} - 12q^{72} + 332q^{73} + 332q^{74} + 240q^{76} + 192q^{77} + 228q^{78} + 342q^{81} + 76q^{82} - 24q^{84} - 76q^{86} - 140q^{88} - 132q^{89} - 336q^{92} - 120q^{93} - 208q^{94} + 156q^{96} - 436q^{97} - 658q^{98} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(300, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
300.3.c.a $$2$$ $$8.174$$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$$
300.3.c.b $$2$$ $$8.174$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$$
300.3.c.c $$2$$ $$8.174$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$$
300.3.c.d $$8$$ $$8.174$$ 8.0.85100625.1 None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+\beta _{6}q^{3}+(1-\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$$
300.3.c.e $$8$$ $$8.174$$ 8.0.4069419264.1 None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}-\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots$$
300.3.c.f $$8$$ $$8.174$$ 8.0.6080256576.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}-\beta _{2}q^{3}+(1-\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots$$
300.3.c.g $$8$$ $$8.174$$ 8.0.4069419264.1 None $$2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(300, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(300, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 2}$$