# Properties

 Label 2450.2.c Level $2450$ Weight $2$ Character orbit 2450.c Rep. character $\chi_{2450}(99,\cdot)$ Character field $\Q$ Dimension $62$ Newform subspaces $24$ Sturm bound $840$ Trace bound $31$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2450 = 2 \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2450.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$24$$ Sturm bound: $$840$$ Trace bound: $$31$$ Distinguishing $$T_p$$: $$3$$, $$11$$, $$13$$, $$19$$, $$31$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2450, [\chi])$$.

Total New Old
Modular forms 468 62 406
Cusp forms 372 62 310
Eisenstein series 96 0 96

## Trace form

 $$62q - 62q^{4} + 2q^{6} - 80q^{9} + O(q^{10})$$ $$62q - 62q^{4} + 2q^{6} - 80q^{9} + 10q^{11} + 62q^{16} - 6q^{19} - 2q^{24} + 4q^{26} - 24q^{29} + 4q^{31} + 2q^{34} + 80q^{36} + 40q^{39} - 14q^{41} - 10q^{44} + 4q^{46} + 34q^{51} - 26q^{54} + 4q^{59} + 32q^{61} - 62q^{64} - 42q^{66} + 12q^{69} + 16q^{71} - 44q^{74} + 6q^{76} - 20q^{79} + 78q^{81} + 8q^{86} - 14q^{89} + 8q^{94} + 2q^{96} - 92q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2450, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2450.2.c.a $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-iq^{8}+\cdots$$
2450.2.c.b $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots$$
2450.2.c.c $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots$$
2450.2.c.d $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots$$
2450.2.c.e $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots$$
2450.2.c.f $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots$$
2450.2.c.g $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}+2q^{9}+\cdots$$
2450.2.c.h $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}+2q^{9}+\cdots$$
2450.2.c.i $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}+iq^{8}+3q^{9}-2q^{11}+\cdots$$
2450.2.c.j $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}-iq^{8}+3q^{9}-2q^{11}+\cdots$$
2450.2.c.k $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}-iq^{8}+3q^{9}+4q^{11}+\cdots$$
2450.2.c.l $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}+2q^{9}+\cdots$$
2450.2.c.m $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}+2q^{9}+\cdots$$
2450.2.c.n $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots$$
2450.2.c.o $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots$$
2450.2.c.p $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots$$
2450.2.c.q $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots$$
2450.2.c.r $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+3iq^{3}-q^{4}+3q^{6}+iq^{8}+\cdots$$
2450.2.c.s $$2$$ $$19.563$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}+3iq^{3}-q^{4}+3q^{6}+iq^{8}+\cdots$$
2450.2.c.t $$4$$ $$19.563$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{2}+(2\zeta_{8}-\zeta_{8}^{2})q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots$$
2450.2.c.u $$4$$ $$19.563$$ $$\Q(i, \sqrt{7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}-\beta _{1}q^{8}+\cdots$$
2450.2.c.v $$4$$ $$19.563$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots$$
2450.2.c.w $$4$$ $$19.563$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{2}+(2\zeta_{8}-\zeta_{8}^{2})q^{3}-q^{4}+(2+\cdots)q^{6}+\cdots$$
2450.2.c.x $$8$$ $$19.563$$ 8.0.959512576.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{3}-\beta _{7})q^{3}-q^{4}+\beta _{6}q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2450, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2450, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(245, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(490, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1225, [\chi])$$$$^{\oplus 2}$$