# Properties

 Label 3150.2.g Level $3150$ Weight $2$ Character orbit 3150.g Rep. character $\chi_{3150}(2899,\cdot)$ Character field $\Q$ Dimension $44$ Newform subspaces $22$ Sturm bound $1440$ Trace bound $26$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3150.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$22$$ Sturm bound: $$1440$$ Trace bound: $$26$$ Distinguishing $$T_p$$: $$11$$, $$13$$, $$17$$, $$19$$, $$29$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3150, [\chi])$$.

Total New Old
Modular forms 768 44 724
Cusp forms 672 44 628
Eisenstein series 96 0 96

## Trace form

 $$44 q - 44 q^{4} + O(q^{10})$$ $$44 q - 44 q^{4} - 4 q^{11} - 4 q^{14} + 44 q^{16} - 16 q^{19} - 12 q^{26} + 16 q^{29} - 40 q^{31} + 28 q^{34} - 44 q^{41} + 4 q^{44} - 16 q^{46} - 44 q^{49} + 4 q^{56} + 20 q^{59} + 36 q^{61} - 44 q^{64} + 24 q^{71} + 16 q^{74} + 16 q^{76} - 56 q^{79} + 56 q^{86} - 36 q^{89} + 20 q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3150, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3150.2.g.a $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}-iq^{7}+iq^{8}-6q^{11}+\cdots$$
3150.2.g.b $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}-iq^{7}+iq^{8}-4q^{11}+\cdots$$
3150.2.g.c $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}+iq^{7}-iq^{8}-4q^{11}+\cdots$$
3150.2.g.d $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}+iq^{7}-iq^{8}-4q^{11}+\cdots$$
3150.2.g.e $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}-iq^{7}-iq^{8}-4q^{11}+\cdots$$
3150.2.g.f $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}-iq^{7}-iq^{8}-3q^{11}+\cdots$$
3150.2.g.g $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}+iq^{7}-iq^{8}-2q^{11}+\cdots$$
3150.2.g.h $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}+iq^{7}+iq^{8}-2q^{11}+\cdots$$
3150.2.g.i $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}-iq^{7}+iq^{8}+2iq^{13}+\cdots$$
3150.2.g.j $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}-iq^{7}+iq^{8}-4iq^{13}+\cdots$$
3150.2.g.k $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}-iq^{7}+iq^{8}-iq^{13}+\cdots$$
3150.2.g.l $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}+iq^{7}-iq^{8}-2iq^{13}+\cdots$$
3150.2.g.m $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}-iq^{7}-iq^{8}+2iq^{13}+\cdots$$
3150.2.g.n $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}-iq^{7}-iq^{8}-iq^{13}+\cdots$$
3150.2.g.o $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}-iq^{7}-iq^{8}+2iq^{13}+\cdots$$
3150.2.g.p $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}+iq^{7}+iq^{8}+2q^{11}+\cdots$$
3150.2.g.q $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}+iq^{7}-iq^{8}+4q^{11}+\cdots$$
3150.2.g.r $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}-iq^{7}+iq^{8}+4q^{11}+\cdots$$
3150.2.g.s $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}+iq^{7}+iq^{8}+4q^{11}+\cdots$$
3150.2.g.t $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-q^{4}-iq^{7}-iq^{8}+4q^{11}+\cdots$$
3150.2.g.u $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}+iq^{7}+iq^{8}+4q^{11}+\cdots$$
3150.2.g.v $2$ $25.153$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}-iq^{7}+iq^{8}+5q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(3150, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3150, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(450, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(630, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1050, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1575, [\chi])$$$$^{\oplus 2}$$