# Properties

 Label 2205.2.d Level $2205$ Weight $2$ Character orbit 2205.d Rep. character $\chi_{2205}(1324,\cdot)$ Character field $\Q$ Dimension $98$ Newform subspaces $20$ Sturm bound $672$ Trace bound $16$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2205 = 3^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2205.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$20$$ Sturm bound: $$672$$ Trace bound: $$16$$ Distinguishing $$T_p$$: $$2$$, $$11$$, $$13$$, $$19$$, $$29$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2205, [\chi])$$.

Total New Old
Modular forms 368 108 260
Cusp forms 304 98 206
Eisenstein series 64 10 54

## Trace form

 $$98 q - 94 q^{4} + O(q^{10})$$ $$98 q - 94 q^{4} - 2 q^{10} - 8 q^{11} + 86 q^{16} + 8 q^{19} - 20 q^{20} - 6 q^{25} + 28 q^{26} + 28 q^{29} + 12 q^{31} - 16 q^{34} + 6 q^{40} + 12 q^{41} + 24 q^{44} + 76 q^{46} - 4 q^{50} - 4 q^{55} - 36 q^{59} - 12 q^{61} - 94 q^{64} + 32 q^{65} + 16 q^{71} - 8 q^{74} - 40 q^{76} + 16 q^{79} + 60 q^{80} + 24 q^{85} + 20 q^{86} - 40 q^{89} - 52 q^{94} + 68 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2205, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2205.2.d.a $2$ $17.607$ $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{-15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{2}-3q^{4}+\beta q^{5}-\beta q^{8}-5q^{10}+\cdots$$
2205.2.d.b $2$ $17.607$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+2iq^{2}-2q^{4}+(-2+i)q^{5}+(-2+\cdots)q^{10}+\cdots$$
2205.2.d.c $2$ $17.607$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{2}+q^{4}+(-2-i)q^{5}+3iq^{8}+\cdots$$
2205.2.d.d $2$ $17.607$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}+q^{4}+(-1-2i)q^{5}+3iq^{8}+\cdots$$
2205.2.d.e $2$ $17.607$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{2}+q^{4}+(1+2i)q^{5}+3iq^{8}+\cdots$$
2205.2.d.f $2$ $17.607$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{2}+q^{4}+(1+2i)q^{5}+3iq^{8}+\cdots$$
2205.2.d.g $2$ $17.607$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{2}+q^{4}+(2-i)q^{5}+3iq^{8}+(1+\cdots)q^{10}+\cdots$$
2205.2.d.h $2$ $17.607$ $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{-35})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{4}+\beta q^{5}+3q^{11}+3\beta q^{13}+4q^{16}+\cdots$$
2205.2.d.i $4$ $17.607$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-4q^{4}+(-\beta _{1}+\beta _{2})q^{5}-2\beta _{3}q^{8}+\cdots$$
2205.2.d.j $4$ $17.607$ $$\Q(\sqrt{-3}, \sqrt{-5})$$ $$\Q(\sqrt{-15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}-q^{4}+\beta _{1}q^{5}+\beta _{2}q^{8}-\beta _{3}q^{10}+\cdots$$
2205.2.d.k $4$ $17.607$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{2}+q^{4}+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+3\zeta_{8}^{2}q^{8}+\cdots$$
2205.2.d.l $6$ $17.607$ 6.0.350464.1 None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{1}q^{2}+(-1-\beta _{2}+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$$
2205.2.d.m $8$ $17.607$ 8.0.309760000.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}+(-2-\beta _{1})q^{4}+\beta _{2}q^{5}+(-\beta _{5}+\cdots)q^{8}+\cdots$$
2205.2.d.n $8$ $17.607$ 8.0.3317760000.3 $$\Q(\sqrt{-15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+(-2+\beta _{2})q^{4}+\beta _{6}q^{5}+(4\beta _{3}+\cdots)q^{8}+\cdots$$
2205.2.d.o $8$ $17.607$ 8.0.2058981376.2 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots$$
2205.2.d.p $8$ $17.607$ 8.0.$$\cdots$$.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}+(-1-\beta _{3})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
2205.2.d.q $8$ $17.607$ 8.0.$$\cdots$$.4 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}-q^{4}+\beta _{7}q^{5}+\beta _{2}q^{8}+(-\beta _{3}+\cdots)q^{10}+\cdots$$
2205.2.d.r $8$ $17.607$ 8.0.$$\cdots$$.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}+(-1-\beta _{3})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$
2205.2.d.s $8$ $17.607$ 8.0.2058981376.2 None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots$$
2205.2.d.t $8$ $17.607$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{24}^{3}-\zeta_{24}^{5})q^{2}-\zeta_{24}^{4}q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2205, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2205, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(245, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(735, [\chi])$$$$^{\oplus 2}$$