# Properties

 Label 1045.2.b Level $1045$ Weight $2$ Character orbit 1045.b Rep. character $\chi_{1045}(419,\cdot)$ Character field $\Q$ Dimension $92$ Newform subspaces $5$ Sturm bound $240$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1045 = 5 \cdot 11 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1045.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$240$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1045, [\chi])$$.

Total New Old
Modular forms 124 92 32
Cusp forms 116 92 24
Eisenstein series 8 0 8

## Trace form

 $$92 q - 96 q^{4} + 6 q^{5} - 8 q^{6} - 96 q^{9} + O(q^{10})$$ $$92 q - 96 q^{4} + 6 q^{5} - 8 q^{6} - 96 q^{9} + 8 q^{10} + 8 q^{11} + 16 q^{14} - 6 q^{15} + 96 q^{16} - 16 q^{20} - 32 q^{21} + 24 q^{24} - 10 q^{25} + 40 q^{29} - 32 q^{30} + 4 q^{31} - 56 q^{34} - 24 q^{35} + 192 q^{36} - 32 q^{40} - 8 q^{41} - 12 q^{44} - 4 q^{45} + 56 q^{46} - 76 q^{49} - 8 q^{50} + 48 q^{51} - 72 q^{54} - 6 q^{55} + 24 q^{56} + 28 q^{59} - 16 q^{60} + 8 q^{61} - 104 q^{64} + 60 q^{65} + 16 q^{66} - 44 q^{69} - 60 q^{70} - 52 q^{71} - 16 q^{74} - 2 q^{75} - 24 q^{79} + 76 q^{80} + 36 q^{81} - 136 q^{84} - 48 q^{85} + 64 q^{86} + 44 q^{89} + 80 q^{90} + 64 q^{91} + 24 q^{94} + 24 q^{96} - 4 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1045, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1045.2.b.a $4$ $8.344$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots$$
1045.2.b.b $16$ $8.344$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$3$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{11}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{13}+\cdots)q^{5}+\cdots$$
1045.2.b.c $20$ $8.344$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2})q^{4}-\beta _{11}q^{5}+\cdots$$
1045.2.b.d $22$ $8.344$ None $$0$$ $$0$$ $$7$$ $$0$$
1045.2.b.e $30$ $8.344$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1045, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1045, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 2}$$