# Properties

 Label 3360.2.t Level $3360$ Weight $2$ Character orbit 3360.t Rep. character $\chi_{3360}(2689,\cdot)$ Character field $\Q$ Dimension $72$ Newform subspaces $14$ Sturm bound $1536$ Trace bound $29$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3360.t (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$14$$ Sturm bound: $$1536$$ Trace bound: $$29$$ Distinguishing $$T_p$$: $$11$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3360, [\chi])$$.

Total New Old
Modular forms 800 72 728
Cusp forms 736 72 664
Eisenstein series 64 0 64

## Trace form

 $$72 q + 8 q^{5} - 72 q^{9} + O(q^{10})$$ $$72 q + 8 q^{5} - 72 q^{9} + 24 q^{25} - 16 q^{29} - 48 q^{41} - 8 q^{45} - 72 q^{49} + 16 q^{61} + 72 q^{81} + 16 q^{85} + 48 q^{89} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3360, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3360.2.t.a $2$ $26.830$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{3}+(-2-i)q^{5}+iq^{7}-q^{9}+\cdots$$
3360.2.t.b $2$ $26.830$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-iq^{3}+(-2-i)q^{5}-iq^{7}-q^{9}+\cdots$$
3360.2.t.c $2$ $26.830$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-iq^{3}+(1-2i)q^{5}-iq^{7}-q^{9}-6q^{11}+\cdots$$
3360.2.t.d $2$ $26.830$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1-2i)q^{5}+iq^{7}-q^{9}-2q^{11}+\cdots$$
3360.2.t.e $2$ $26.830$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1+2i)q^{5}+iq^{7}-q^{9}+2q^{11}+\cdots$$
3360.2.t.f $2$ $26.830$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-iq^{3}+(1+2i)q^{5}-iq^{7}-q^{9}+6q^{11}+\cdots$$
3360.2.t.g $4$ $26.830$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}-q^{9}+2\beta _{2}q^{13}+\cdots$$
3360.2.t.h $6$ $26.830$ 6.0.350464.1 None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{1}q^{7}-q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$$
3360.2.t.i $6$ $26.830$ 6.0.350464.1 None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}-q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots$$
3360.2.t.j $8$ $26.830$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{20}q^{3}-\zeta_{20}^{3}q^{5}+\zeta_{20}q^{7}-q^{9}+\cdots$$
3360.2.t.k $8$ $26.830$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}q^{3}-\zeta_{24}^{6}q^{5}-\zeta_{24}q^{7}-q^{9}+\cdots$$
3360.2.t.l $8$ $26.830$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}q^{3}-\zeta_{24}^{3}q^{5}-\zeta_{24}q^{7}-q^{9}+\cdots$$
3360.2.t.m $10$ $26.830$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{5}q^{5}-\beta _{1}q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots$$
3360.2.t.n $10$ $26.830$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{5}q^{5}+\beta _{1}q^{7}-q^{9}+(1+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(3360, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3360, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(420, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(480, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(560, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(840, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1120, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1680, [\chi])$$$$^{\oplus 2}$$