# Properties

 Label 100.4.c Level $100$ Weight $4$ Character orbit 100.c Rep. character $\chi_{100}(49,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $60$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$100 = 2^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 100.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$60$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(100, [\chi])$$.

Total New Old
Modular forms 54 4 50
Cusp forms 36 4 32
Eisenstein series 18 0 18

## Trace form

 $$4 q + 74 q^{9} + O(q^{10})$$ $$4 q + 74 q^{9} - 30 q^{11} + 94 q^{19} - 76 q^{21} + 84 q^{29} + 404 q^{31} - 776 q^{39} - 546 q^{41} - 492 q^{49} + 378 q^{51} + 648 q^{59} - 352 q^{61} - 348 q^{69} + 552 q^{71} + 1252 q^{79} + 676 q^{81} + 1326 q^{89} - 464 q^{91} + 1020 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(100, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.4.c.a $2$ $5.900$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}+8iq^{7}+11q^{9}-60q^{11}+\cdots$$
100.4.c.b $2$ $5.900$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-26iq^{7}+26q^{9}+45q^{11}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(100, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(100, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(10, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 2}$$