# Properties

 Label 3822.2.c Level $3822$ Weight $2$ Character orbit 3822.c Rep. character $\chi_{3822}(883,\cdot)$ Character field $\Q$ Dimension $98$ Newform subspaces $16$ Sturm bound $1568$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3822.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$16$$ Sturm bound: $$1568$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$17$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3822, [\chi])$$.

Total New Old
Modular forms 816 98 718
Cusp forms 752 98 654
Eisenstein series 64 0 64

## Trace form

 $$98 q - 2 q^{3} - 98 q^{4} + 98 q^{9} + O(q^{10})$$ $$98 q - 2 q^{3} - 98 q^{4} + 98 q^{9} + 4 q^{10} + 2 q^{12} - 10 q^{13} + 98 q^{16} - 12 q^{17} + 8 q^{22} - 8 q^{23} - 126 q^{25} - 4 q^{26} - 2 q^{27} + 4 q^{29} - 4 q^{30} - 98 q^{36} + 4 q^{38} - 14 q^{39} - 4 q^{40} - 56 q^{43} - 2 q^{48} - 4 q^{51} + 10 q^{52} + 60 q^{53} + 64 q^{55} - 20 q^{61} + 20 q^{62} - 98 q^{64} + 72 q^{65} - 16 q^{66} + 12 q^{68} + 8 q^{69} - 48 q^{74} - 2 q^{75} - 4 q^{78} + 48 q^{79} + 98 q^{81} + 28 q^{82} + 28 q^{87} - 8 q^{88} + 4 q^{90} + 8 q^{92} - 16 q^{94} - 72 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3822, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3822.2.c.a $2$ $30.519$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+iq^{2}-q^{3}-q^{4}+3iq^{5}-iq^{6}+\cdots$$
3822.2.c.b $2$ $30.519$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}-iq^{8}+\cdots$$
3822.2.c.c $2$ $30.519$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}-q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots$$
3822.2.c.d $2$ $30.519$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-iq^{2}-q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots$$
3822.2.c.e $2$ $30.519$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+iq^{2}+q^{3}-q^{4}+iq^{5}+iq^{6}-iq^{8}+\cdots$$
3822.2.c.f $4$ $30.519$ $$\Q(i, \sqrt{10})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-q^{3}-q^{4}+(\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots$$
3822.2.c.g $4$ $30.519$ $$\Q(i, \sqrt{10})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+q^{3}-q^{4}+(\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots$$
3822.2.c.h $4$ $30.519$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+q^{3}-q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$$
3822.2.c.i $6$ $30.519$ 6.0.3356224.1 None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-q^{3}-q^{4}+(-\beta _{1}+\beta _{4})q^{5}+\cdots$$
3822.2.c.j $6$ $30.519$ 6.0.9144576.1 None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}-q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots$$
3822.2.c.k $6$ $30.519$ 6.0.9144576.1 None $$0$$ $$6$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots$$
3822.2.c.l $6$ $30.519$ 6.0.3356224.1 None $$0$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+q^{3}-q^{4}+(-\beta _{1}+\beta _{4})q^{5}+\cdots$$
3822.2.c.m $10$ $30.519$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$-10$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}-q^{3}-q^{4}+\beta _{1}q^{5}+\beta _{4}q^{6}+\cdots$$
3822.2.c.n $10$ $30.519$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$10$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+q^{3}-q^{4}+\beta _{1}q^{5}+\beta _{4}q^{6}+\cdots$$
3822.2.c.o $16$ $30.519$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$-16$$ $$0$$ $$0$$ $$q+\beta _{7}q^{2}-q^{3}-q^{4}-\beta _{4}q^{5}-\beta _{7}q^{6}+\cdots$$
3822.2.c.p $16$ $30.519$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$16$$ $$0$$ $$0$$ $$q-\beta _{7}q^{2}+q^{3}-q^{4}-\beta _{4}q^{5}-\beta _{7}q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(3822, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3822, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1274, [\chi])$$$$^{\oplus 2}$$