# Properties

 Label 1900.2.s Level $1900$ Weight $2$ Character orbit 1900.s Rep. character $\chi_{1900}(49,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $60$ Newform subspaces $5$ Sturm bound $600$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1900 = 2^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1900.s (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$600$$ Trace bound: $$9$$ 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

 $$60 q + 30 q^{9} + O(q^{10})$$ $$60 q + 30 q^{9} + 4 q^{11} - 4 q^{19} + 2 q^{21} + 16 q^{29} + 4 q^{31} - 20 q^{39} - 36 q^{41} - 52 q^{49} - 4 q^{51} - 30 q^{59} - 8 q^{61} - 56 q^{69} + 10 q^{71} + 8 q^{79} - 70 q^{81} + 50 q^{89} - 34 q^{91} + 4 q^{99} + O(q^{100})$$

## 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.s.a $4$ $15.172$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}-2\zeta_{12}^{2}q^{9}-4q^{11}+(-\zeta_{12}+\cdots)q^{13}+\cdots$$
1900.2.s.b $4$ $15.172$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}-2\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}+\cdots$$
1900.2.s.c $12$ $15.172$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{6}+\beta _{11})q^{3}+(\beta _{10}+\beta _{11})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots$$
1900.2.s.d $16$ $15.172$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}+\beta _{14}q^{7}+(\beta _{4}-\beta _{5}+\beta _{10}+\cdots)q^{9}+\cdots$$
1900.2.s.e $24$ $15.172$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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