# Properties

 Label 1960.2.q Level $1960$ Weight $2$ Character orbit 1960.q Rep. character $\chi_{1960}(361,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $80$ Newform subspaces $25$ Sturm bound $672$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1960 = 2^{3} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1960.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$25$$ Sturm bound: $$672$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1960, [\chi])$$.

Total New Old
Modular forms 736 80 656
Cusp forms 608 80 528
Eisenstein series 128 0 128

## Trace form

 $$80 q - 4 q^{3} + 2 q^{5} - 42 q^{9} + O(q^{10})$$ $$80 q - 4 q^{3} + 2 q^{5} - 42 q^{9} - 2 q^{11} - 16 q^{13} + 4 q^{17} + 2 q^{19} - 40 q^{25} + 32 q^{27} - 4 q^{29} + 16 q^{31} - 4 q^{37} - 32 q^{39} - 8 q^{41} - 64 q^{43} + 12 q^{45} - 12 q^{47} - 8 q^{51} + 4 q^{53} - 8 q^{57} + 4 q^{59} - 2 q^{61} + 6 q^{65} + 20 q^{67} - 4 q^{69} + 64 q^{71} + 12 q^{73} - 4 q^{75} + 12 q^{79} - 16 q^{81} + 88 q^{83} + 44 q^{87} - 14 q^{89} + 60 q^{93} + 8 q^{95} + 16 q^{97} + 92 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1960, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1960.2.q.a $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$1$$ $$0$$ $$q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots$$
1960.2.q.b $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$-1$$ $$0$$ $$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$$
1960.2.q.c $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$-1$$ $$0$$ $$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$$
1960.2.q.d $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-1$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots$$
1960.2.q.e $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-1$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots$$
1960.2.q.f $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$1$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots$$
1960.2.q.g $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$1$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots$$
1960.2.q.h $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$0$$ $$q-\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots$$
1960.2.q.i $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q+\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots$$
1960.2.q.j $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-1$$ $$0$$ $$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots$$
1960.2.q.k $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-1$$ $$0$$ $$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots$$
1960.2.q.l $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-1$$ $$0$$ $$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(5+\cdots)q^{11}+\cdots$$
1960.2.q.m $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$1$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(5+\cdots)q^{11}+\cdots$$
1960.2.q.n $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$1$$ $$0$$ $$q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots$$
1960.2.q.o $2$ $15.651$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$-1$$ $$0$$ $$q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+(5+\cdots)q^{11}+\cdots$$
1960.2.q.p $4$ $15.651$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$2$$ $$0$$ $$q+(-1+\beta _{1}-\beta _{2})q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\cdots)q^{9}+\cdots$$
1960.2.q.q $4$ $15.651$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$2$$ $$0$$ $$q+(-1+\beta _{1}-\beta _{2})q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\cdots)q^{9}+\cdots$$
1960.2.q.r $4$ $15.651$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$-1$$ $$-2$$ $$0$$ $$q+(-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1})q^{5}+(-5+\cdots)q^{9}+\cdots$$
1960.2.q.s $4$ $15.651$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$0$$ $$-1$$ $$-2$$ $$0$$ $$q-\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(-1+\beta _{1}+\cdots)q^{9}+\cdots$$
1960.2.q.t $4$ $15.651$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$1$$ $$2$$ $$0$$ $$q+\beta _{3}q^{3}+(1-\beta _{1})q^{5}+(-6+5\beta _{1}+\cdots)q^{9}+\cdots$$
1960.2.q.u $4$ $15.651$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$0$$ $$1$$ $$2$$ $$0$$ $$q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$$
1960.2.q.v $4$ $15.651$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$2$$ $$-2$$ $$0$$ $$q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(2\beta _{1}+2\beta _{3})q^{9}+\cdots$$
1960.2.q.w $6$ $15.651$ 6.0.11337408.1 None $$0$$ $$0$$ $$3$$ $$0$$ $$q+(\beta _{3}-\beta _{5})q^{3}+\beta _{1}q^{5}+(-3\beta _{1}-\beta _{4}+\cdots)q^{9}+\cdots$$
1960.2.q.x $8$ $15.651$ 8.0.$$\cdots$$.16 None $$0$$ $$-2$$ $$-4$$ $$0$$ $$q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$$
1960.2.q.y $8$ $15.651$ 8.0.$$\cdots$$.16 None $$0$$ $$2$$ $$4$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{3}q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1960, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1960, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(98, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(196, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(245, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(392, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(490, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(980, [\chi])$$$$^{\oplus 2}$$