# Properties

 Label 6300.2.k Level $6300$ Weight $2$ Character orbit 6300.k Rep. character $\chi_{6300}(6049,\cdot)$ Character field $\Q$ Dimension $44$ Newform subspaces $20$ Sturm bound $2880$ Trace bound $41$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$6300 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 6300.k (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$20$$ Sturm bound: $$2880$$ Trace bound: $$41$$ Distinguishing $$T_p$$: $$11$$, $$13$$, $$17$$, $$41$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(6300, [\chi])$$.

Total New Old
Modular forms 1512 44 1468
Cusp forms 1368 44 1324
Eisenstein series 144 0 144

## Trace form

 $$44 q + O(q^{10})$$ $$44 q + 8 q^{11} + 8 q^{19} - 8 q^{29} - 4 q^{31} + 4 q^{41} - 44 q^{49} - 28 q^{59} - 36 q^{61} - 36 q^{71} + 40 q^{79} + 12 q^{89} - 16 q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(6300, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
6300.2.k.a $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}-6q^{11}-4iq^{13}+6iq^{17}+\cdots$$
6300.2.k.b $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}-4q^{11}+2iq^{17}+6q^{19}+\cdots$$
6300.2.k.c $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}-3q^{11}-iq^{13}-3iq^{17}+\cdots$$
6300.2.k.d $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}-3q^{11}-4iq^{13}-2q^{19}+\cdots$$
6300.2.k.e $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}-2q^{11}-4iq^{13}-6iq^{17}+\cdots$$
6300.2.k.f $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}-2q^{11}-4iq^{13}-2iq^{17}+\cdots$$
6300.2.k.g $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}-2q^{11}+6iq^{13}+4iq^{17}+\cdots$$
6300.2.k.h $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}-q^{11}+4iq^{13}+2iq^{17}+\cdots$$
6300.2.k.i $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}-4iq^{13}+6iq^{17}-2q^{19}+\cdots$$
6300.2.k.j $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+4iq^{13}+6iq^{17}-2q^{19}+\cdots$$
6300.2.k.k $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}+q^{11}+2iq^{13}-6q^{19}+iq^{23}+\cdots$$
6300.2.k.l $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+q^{11}-2iq^{13}+8iq^{17}+\cdots$$
6300.2.k.m $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+2q^{11}-4iq^{13}-2iq^{17}+\cdots$$
6300.2.k.n $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}+3q^{11}-4iq^{13}-6iq^{17}+\cdots$$
6300.2.k.o $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+4q^{11}-2iq^{17}+6q^{19}+\cdots$$
6300.2.k.p $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}+5q^{11}+3iq^{13}+iq^{17}+\cdots$$
6300.2.k.q $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{7}+5q^{11}-6iq^{13}+4iq^{17}+\cdots$$
6300.2.k.r $2$ $50.306$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+6q^{11}-2iq^{13}+4q^{19}+\cdots$$
6300.2.k.s $4$ $50.306$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{7}+\zeta_{12}^{3}q^{11}+2\zeta_{12}q^{13}+\cdots$$
6300.2.k.t $4$ $50.306$ $$\Q(i, \sqrt{7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{7}-\beta _{2}q^{11}+2\beta _{3}q^{17}+3\beta _{3}q^{23}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(6300, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(6300, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(420, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(450, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(630, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(700, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(900, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1050, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1260, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1575, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2100, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(3150, [\chi])$$$$^{\oplus 2}$$