# Properties

 Label 1900.2.l Level $1900$ Weight $2$ Character orbit 1900.l Rep. character $\chi_{1900}(493,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $60$ Newform subspaces $4$ Sturm bound $600$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1900 = 2^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1900.l (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$600$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1900, [\chi])$$.

Total New Old
Modular forms 636 60 576
Cusp forms 564 60 504
Eisenstein series 72 0 72

## Trace form

 $$60 q + 2 q^{7} + O(q^{10})$$ $$60 q + 2 q^{7} - 16 q^{11} - 10 q^{17} - 20 q^{23} + 26 q^{43} + 6 q^{47} - 24 q^{57} + 8 q^{61} - 2 q^{63} + 54 q^{73} - 10 q^{77} + 36 q^{81} - 20 q^{83} + 80 q^{87} - 8 q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1900, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1900.2.l.a $$8$$ $$15.172$$ 8.0.2702336256.1 $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$0$$ $$6$$ $$q+(1+\beta _{1}+\beta _{5})q^{7}-3\beta _{1}q^{9}+(-1+\cdots)q^{11}+\cdots$$
1900.2.l.b $$12$$ $$15.172$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\beta _{2}q^{3}-\beta _{6}q^{7}+(\beta _{3}+4\beta _{5}-\beta _{6}+\cdots)q^{9}+\cdots$$
1900.2.l.c $$16$$ $$15.172$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{3}+\beta _{9}q^{7}+(-\beta _{2}-\beta _{11})q^{9}+\cdots$$
1900.2.l.d $$24$$ $$15.172$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1900, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1900, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(380, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(475, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(950, [\chi])$$$$^{\oplus 2}$$