# Properties

 Label 1900.3.e Level $1900$ Weight $3$ Character orbit 1900.e Rep. character $\chi_{1900}(1101,\cdot)$ Character field $\Q$ Dimension $64$ Newform subspaces $8$ Sturm bound $900$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1900 = 2^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1900.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$900$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(1900, [\chi])$$.

Total New Old
Modular forms 618 64 554
Cusp forms 582 64 518
Eisenstein series 36 0 36

## Trace form

 $$64 q + 9 q^{7} - 202 q^{9} + O(q^{10})$$ $$64 q + 9 q^{7} - 202 q^{9} - q^{11} - 19 q^{17} - 24 q^{19} + 58 q^{23} - 66 q^{39} - 45 q^{43} + 95 q^{47} + 353 q^{49} + 34 q^{57} - 125 q^{61} - 133 q^{63} + 137 q^{73} + 87 q^{77} + 516 q^{81} - 36 q^{83} - 438 q^{87} - 164 q^{93} - 173 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(1900, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1900.3.e.a $$2$$ $$51.771$$ $$\Q(\sqrt{57})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$0$$ $$-5$$ $$q+(-1-3\beta )q^{7}+9q^{9}+(1-5\beta )q^{11}+\cdots$$
1900.3.e.b $$2$$ $$51.771$$ $$\Q(\sqrt{-29})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+\beta q^{3}+q^{7}-20q^{9}+14q^{11}+3\beta q^{13}+\cdots$$
1900.3.e.c $$4$$ $$51.771$$ $$\Q(\sqrt{6}, \sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{2}q^{7}-5q^{9}+4q^{11}-3\beta _{1}q^{13}+\cdots$$
1900.3.e.d $$4$$ $$51.771$$ $$\Q(\sqrt{3}, \sqrt{19})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{7}+9q^{9}+(1-\beta _{3})q^{11}+(\beta _{1}+\cdots)q^{17}+\cdots$$
1900.3.e.e $$12$$ $$51.771$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}+\beta _{8}q^{7}+(-6-\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots$$
1900.3.e.f $$12$$ $$51.771$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$12$$ $$q+\beta _{1}q^{3}+(1+\beta _{9})q^{7}+(-1+\beta _{2})q^{9}+\cdots$$
1900.3.e.g $$14$$ $$51.771$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{3}-\beta _{7}q^{7}+(-4+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots$$
1900.3.e.h $$14$$ $$51.771$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{1}q^{3}+\beta _{7}q^{7}+(-4+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(1900, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(1900, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(380, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(475, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(950, [\chi])$$$$^{\oplus 2}$$