# Properties

 Label 2790.2.d Level $2790$ Weight $2$ Character orbit 2790.d Rep. character $\chi_{2790}(559,\cdot)$ Character field $\Q$ Dimension $76$ Newform subspaces $15$ Sturm bound $1152$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2790.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$15$$ Sturm bound: $$1152$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$7$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2790, [\chi])$$.

Total New Old
Modular forms 592 76 516
Cusp forms 560 76 484
Eisenstein series 32 0 32

## Trace form

 $$76 q - 76 q^{4} - 4 q^{5} + O(q^{10})$$ $$76 q - 76 q^{4} - 4 q^{5} + 12 q^{11} + 8 q^{14} + 76 q^{16} + 16 q^{19} + 4 q^{20} - 12 q^{25} - 12 q^{26} - 4 q^{29} + 8 q^{34} - 8 q^{35} - 16 q^{41} - 12 q^{44} - 16 q^{46} - 92 q^{49} + 16 q^{50} + 36 q^{55} - 8 q^{56} - 32 q^{59} - 36 q^{61} - 76 q^{64} + 28 q^{65} - 32 q^{71} + 4 q^{74} - 16 q^{76} + 24 q^{79} - 4 q^{80} - 12 q^{85} + 20 q^{86} + 72 q^{89} - 64 q^{91} + 32 q^{94} + 24 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2790, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2790.2.d.a $2$ $22.278$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{2}-q^{4}+(-2+i)q^{5}+2iq^{7}+\cdots$$
2790.2.d.b $2$ $22.278$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{2}-q^{4}+(-2+i)q^{5}+2iq^{7}+\cdots$$
2790.2.d.c $2$ $22.278$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-iq^{2}-q^{4}+(-2-i)q^{5}+2iq^{7}+\cdots$$
2790.2.d.d $2$ $22.278$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{2}-q^{4}+(-2-i)q^{5}+2iq^{7}+\cdots$$
2790.2.d.e $2$ $22.278$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}-q^{4}+(-1-2i)q^{5}+5iq^{7}+\cdots$$
2790.2.d.f $2$ $22.278$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-iq^{2}-q^{4}+(1-2i)q^{5}+iq^{7}+iq^{8}+\cdots$$
2790.2.d.g $2$ $22.278$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-iq^{2}-q^{4}+(1+2i)q^{5}+iq^{7}+iq^{8}+\cdots$$
2790.2.d.h $2$ $22.278$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q-iq^{2}-q^{4}+(2-i)q^{5}+2iq^{7}+iq^{8}+\cdots$$
2790.2.d.i $4$ $22.278$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$-8$$ $$0$$ $$q-\zeta_{8}q^{2}-q^{4}+(-2-\zeta_{8})q^{5}+(2\zeta_{8}+\cdots)q^{7}+\cdots$$
2790.2.d.j $6$ $22.278$ 6.0.11669056.1 None $$0$$ $$0$$ $$4$$ $$0$$ $$q-\beta _{3}q^{2}-q^{4}+(1-\beta _{1})q^{5}+2\beta _{3}q^{7}+\cdots$$
2790.2.d.k $6$ $22.278$ 6.0.3534400.1 None $$0$$ $$0$$ $$6$$ $$0$$ $$q-\beta _{5}q^{2}-q^{4}+(1-\beta _{4})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$$
2790.2.d.l $8$ $22.278$ 8.0.2058981376.2 None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{4}q^{2}-q^{4}+(1+\beta _{1}-\beta _{7})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$$
2790.2.d.m $8$ $22.278$ 8.0.619810816.2 None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{2}q^{2}-q^{4}+(\beta _{6}+\beta _{7})q^{5}+(\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$$
2790.2.d.n $12$ $22.278$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(\beta _{6}+\beta _{7}+\beta _{11})q^{7}+\cdots$$
2790.2.d.o $16$ $22.278$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{9}q^{2}-q^{4}+\beta _{6}q^{5}-\beta _{1}q^{7}-\beta _{9}q^{8}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2790, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2790, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(155, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(310, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(465, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(930, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1395, [\chi])$$$$^{\oplus 2}$$