# Properties

 Label 4100.2.d Level $4100$ Weight $2$ Character orbit 4100.d Rep. character $\chi_{4100}(1149,\cdot)$ Character field $\Q$ Dimension $60$ Newform subspaces $7$ Sturm bound $1260$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$4100 = 2^{2} \cdot 5^{2} \cdot 41$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4100.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$1260$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(4100, [\chi])$$.

Total New Old
Modular forms 648 60 588
Cusp forms 612 60 552
Eisenstein series 36 0 36

## Trace form

 $$60q - 56q^{9} + O(q^{10})$$ $$60q - 56q^{9} - 8q^{11} - 4q^{21} + 20q^{29} + 24q^{31} - 12q^{39} - 8q^{41} - 76q^{49} + 4q^{51} + 8q^{59} + 16q^{61} - 28q^{69} + 60q^{71} + 40q^{79} + 108q^{81} - 20q^{91} + 20q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(4100, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
4100.2.d.a $$4$$ $$32.739$$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+2q^{9}+(-1+\cdots)q^{11}+\cdots$$
4100.2.d.b $$4$$ $$32.739$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}+(\beta _{1}+\beta _{3})q^{7}+2q^{9}+(3+4\beta _{2}+\cdots)q^{11}+\cdots$$
4100.2.d.c $$8$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}-\beta _{4}+\beta _{6})q^{3}+(\beta _{2}-\beta _{4}-\beta _{7})q^{7}+\cdots$$
4100.2.d.d $$8$$ $$32.739$$ 8.0.4569760000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(\beta _{1}+\beta _{5})q^{7}+(-1+\beta _{4}+\cdots)q^{9}+\cdots$$
4100.2.d.e $$8$$ $$32.739$$ 8.0.2732361984.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{3}+\beta _{5}q^{7}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$$
4100.2.d.f $$14$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{11}q^{7}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots$$
4100.2.d.g $$14$$ $$32.739$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{7}q^{7}+(\beta _{2}+\beta _{3})q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(4100, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(4100, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(205, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(410, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(820, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1025, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2050, [\chi])$$$$^{\oplus 2}$$