# Properties

 Label 825.2.bx Level $825$ Weight $2$ Character orbit 825.bx Rep. character $\chi_{825}(49,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $144$ Newform subspaces $10$ Sturm bound $240$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$825 = 3 \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 825.bx (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$10$$ Sturm bound: $$240$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$2$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(825, [\chi])$$.

Total New Old
Modular forms 528 144 384
Cusp forms 432 144 288
Eisenstein series 96 0 96

## Trace form

 $$144 q + 36 q^{4} - 4 q^{6} + 36 q^{9} + O(q^{10})$$ $$144 q + 36 q^{4} - 4 q^{6} + 36 q^{9} + 4 q^{11} + 8 q^{14} + 4 q^{16} + 8 q^{19} + 32 q^{21} + 12 q^{24} + 92 q^{26} + 28 q^{31} + 48 q^{34} - 36 q^{36} - 96 q^{41} - 108 q^{44} - 4 q^{46} + 104 q^{49} - 40 q^{51} - 16 q^{54} - 168 q^{56} - 84 q^{59} - 52 q^{61} + 76 q^{64} - 16 q^{66} - 28 q^{69} + 48 q^{71} + 96 q^{74} + 184 q^{76} + 56 q^{79} - 36 q^{81} - 24 q^{84} + 56 q^{86} - 80 q^{89} + 60 q^{91} - 108 q^{94} - 28 q^{96} - 4 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(825, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
825.2.bx.a $8$ $6.588$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{20}+\zeta_{20}^{5})q^{2}+(-\zeta_{20}+\zeta_{20}^{3}+\cdots)q^{3}+\cdots$$
825.2.bx.b $8$ $6.588$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{20}+\zeta_{20}^{5})q^{2}+(-\zeta_{20}+\zeta_{20}^{3}+\cdots)q^{3}+\cdots$$
825.2.bx.c $8$ $6.588$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5})q^{2}+(-\zeta_{20}+\cdots)q^{3}+\cdots$$
825.2.bx.d $8$ $6.588$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(2\zeta_{20}+\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+\zeta_{20}^{3}q^{3}+\cdots$$
825.2.bx.e $16$ $6.588$ $$\Q(\zeta_{60})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{60}^{11}-\zeta_{60}^{13})q^{2}+(\zeta_{60}-\zeta_{60}^{11}+\cdots)q^{3}+\cdots$$
825.2.bx.f $16$ $6.588$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{11}-\beta _{13})q^{2}-\beta _{15}q^{3}+(-\beta _{5}+\cdots)q^{4}+\cdots$$
825.2.bx.g $16$ $6.588$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{10}q^{2}+\beta _{11}q^{3}+(2\beta _{2}-\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots$$
825.2.bx.h $16$ $6.588$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{8}+\beta _{13}-2\beta _{15})q^{2}-\beta _{14}q^{3}+\cdots$$
825.2.bx.i $16$ $6.588$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{15}q^{2}+\beta _{9}q^{3}+(2-2\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots$$
825.2.bx.j $32$ $6.588$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(825, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(825, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(165, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(275, [\chi])$$$$^{\oplus 2}$$