# Properties

 Label 465.2.c Level $465$ Weight $2$ Character orbit 465.c Rep. character $\chi_{465}(94,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $2$ Sturm bound $128$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$465 = 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 465.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$128$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(465, [\chi])$$.

Total New Old
Modular forms 68 32 36
Cusp forms 60 32 28
Eisenstein series 8 0 8

## Trace form

 $$32 q - 36 q^{4} - 32 q^{9} + O(q^{10})$$ $$32 q - 36 q^{4} - 32 q^{9} - 2 q^{10} - 4 q^{14} + 4 q^{15} + 60 q^{16} - 16 q^{19} + 14 q^{20} - 12 q^{25} - 24 q^{26} + 8 q^{29} + 8 q^{30} + 12 q^{31} - 16 q^{34} + 36 q^{36} - 16 q^{39} - 8 q^{40} - 16 q^{41} + 40 q^{44} - 16 q^{46} - 24 q^{49} + 22 q^{50} + 8 q^{51} + 28 q^{55} - 48 q^{56} - 8 q^{59} - 12 q^{60} - 80 q^{64} + 44 q^{65} + 8 q^{66} - 16 q^{69} + 14 q^{70} - 24 q^{71} + 88 q^{74} - 8 q^{75} + 4 q^{76} + 32 q^{79} - 70 q^{80} + 32 q^{81} - 8 q^{84} - 8 q^{85} - 16 q^{86} + 8 q^{89} + 2 q^{90} - 8 q^{91} - 16 q^{94} + 16 q^{95} + 40 q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(465, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
465.2.c.a $10$ $3.713$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}+\beta _{8})q^{2}+\beta _{3}q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$$
465.2.c.b $22$ $3.713$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(465, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(465, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(155, [\chi])$$$$^{\oplus 2}$$