# Properties

 Label 1050.3.h Level $1050$ Weight $3$ Character orbit 1050.h Rep. character $\chi_{1050}(349,\cdot)$ Character field $\Q$ Dimension $48$ Newform subspaces $3$ Sturm bound $720$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1050.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$720$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(1050, [\chi])$$.

Total New Old
Modular forms 504 48 456
Cusp forms 456 48 408
Eisenstein series 48 0 48

## Trace form

 $$48 q - 96 q^{4} + 144 q^{9} + O(q^{10})$$ $$48 q - 96 q^{4} + 144 q^{9} - 112 q^{11} - 32 q^{14} + 192 q^{16} + 12 q^{21} - 48 q^{29} - 288 q^{36} - 72 q^{39} + 224 q^{44} + 272 q^{46} - 148 q^{49} + 96 q^{51} + 64 q^{56} - 384 q^{64} + 608 q^{71} - 128 q^{74} + 736 q^{79} + 432 q^{81} - 24 q^{84} - 352 q^{86} - 188 q^{91} - 336 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(1050, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1050.3.h.a $8$ $28.610$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}q^{2}-\zeta_{24}^{2}q^{3}-2q^{4}-\zeta_{24}^{7}q^{6}+\cdots$$
1050.3.h.b $16$ $28.610$ 16.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}-\beta _{3}q^{3}-2q^{4}+\beta _{11}q^{6}+\cdots$$
1050.3.h.c $24$ $28.610$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{3}^{\mathrm{old}}(1050, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(1050, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 2}$$