# Properties

 Label 2394.2.b Level $2394$ Weight $2$ Character orbit 2394.b Rep. character $\chi_{2394}(1709,\cdot)$ Character field $\Q$ Dimension $40$ Newform subspaces $10$ Sturm bound $960$ Trace bound $25$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2394.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q$$ Newform subspaces: $$10$$ Sturm bound: $$960$$ Trace bound: $$25$$ Distinguishing $$T_p$$: $$5$$, $$29$$, $$53$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2394, [\chi])$$.

Total New Old
Modular forms 496 40 456
Cusp forms 464 40 424
Eisenstein series 32 0 32

## Trace form

 $$40 q + 40 q^{4} + O(q^{10})$$ $$40 q + 40 q^{4} + 40 q^{16} + 16 q^{19} - 56 q^{25} - 32 q^{43} + 40 q^{49} + 16 q^{58} + 80 q^{61} + 40 q^{64} + 16 q^{73} + 16 q^{76} + 16 q^{82} + 96 q^{85} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2394, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2394.2.b.a $2$ $19.116$ $$\Q(\sqrt{-2})$$ None $$-2$$ $$0$$ $$0$$ $$-2$$ $$q-q^{2}+q^{4}-q^{7}-q^{8}-\beta q^{13}+q^{14}+\cdots$$
2394.2.b.b $2$ $19.116$ $$\Q(\sqrt{-2})$$ None $$-2$$ $$0$$ $$0$$ $$2$$ $$q-q^{2}+q^{4}+2\beta q^{5}+q^{7}-q^{8}-2\beta q^{10}+\cdots$$
2394.2.b.c $2$ $19.116$ $$\Q(\sqrt{-2})$$ None $$-2$$ $$0$$ $$0$$ $$2$$ $$q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots$$
2394.2.b.d $2$ $19.116$ $$\Q(\sqrt{-2})$$ None $$2$$ $$0$$ $$0$$ $$-2$$ $$q+q^{2}+q^{4}-q^{7}+q^{8}-\beta q^{13}-q^{14}+\cdots$$
2394.2.b.e $2$ $19.116$ $$\Q(\sqrt{-2})$$ None $$2$$ $$0$$ $$0$$ $$2$$ $$q+q^{2}+q^{4}+2\beta q^{5}+q^{7}+q^{8}+2\beta q^{10}+\cdots$$
2394.2.b.f $2$ $19.116$ $$\Q(\sqrt{-2})$$ None $$2$$ $$0$$ $$0$$ $$2$$ $$q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots$$
2394.2.b.g $6$ $19.116$ 6.0.2803712.1 None $$-6$$ $$0$$ $$0$$ $$6$$ $$q-q^{2}+q^{4}-\beta _{1}q^{5}+q^{7}-q^{8}+\beta _{1}q^{10}+\cdots$$
2394.2.b.h $6$ $19.116$ 6.0.2803712.1 None $$6$$ $$0$$ $$0$$ $$6$$ $$q+q^{2}+q^{4}-\beta _{1}q^{5}+q^{7}+q^{8}-\beta _{1}q^{10}+\cdots$$
2394.2.b.i $8$ $19.116$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$-8$$ $$0$$ $$0$$ $$-8$$ $$q-q^{2}+q^{4}+\beta _{3}q^{5}-q^{7}-q^{8}-\beta _{3}q^{10}+\cdots$$
2394.2.b.j $8$ $19.116$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$8$$ $$0$$ $$0$$ $$-8$$ $$q+q^{2}+q^{4}+\beta _{3}q^{5}-q^{7}+q^{8}+\beta _{3}q^{10}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2394, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2394, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(342, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(399, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(798, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1197, [\chi])$$$$^{\oplus 2}$$