# Properties

 Label 1150.4.b Level $1150$ Weight $4$ Character orbit 1150.b Rep. character $\chi_{1150}(599,\cdot)$ Character field $\Q$ Dimension $100$ Newform subspaces $19$ Sturm bound $720$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1150 = 2 \cdot 5^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1150.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$19$$ Sturm bound: $$720$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(1150, [\chi])$$.

Total New Old
Modular forms 552 100 452
Cusp forms 528 100 428
Eisenstein series 24 0 24

## Trace form

 $$100 q - 400 q^{4} + 24 q^{6} - 808 q^{9} + O(q^{10})$$ $$100 q - 400 q^{4} + 24 q^{6} - 808 q^{9} - 32 q^{11} + 1600 q^{16} - 144 q^{19} + 448 q^{21} - 96 q^{24} + 384 q^{26} - 944 q^{29} - 872 q^{31} + 680 q^{34} + 3232 q^{36} - 1168 q^{39} + 756 q^{41} + 128 q^{44} + 184 q^{46} - 4564 q^{49} + 2524 q^{51} - 216 q^{54} - 2296 q^{59} - 932 q^{61} - 6400 q^{64} - 1064 q^{66} - 552 q^{69} - 1576 q^{71} + 2616 q^{74} + 576 q^{76} + 4600 q^{79} + 11060 q^{81} - 1792 q^{84} - 2360 q^{86} + 6764 q^{89} - 6600 q^{91} - 480 q^{94} + 384 q^{96} - 3140 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(1150, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1150.4.b.a $2$ $67.852$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}+9iq^{3}-4q^{4}-18q^{6}+2iq^{7}+\cdots$$
1150.4.b.b $2$ $67.852$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}+7iq^{3}-4q^{4}-14q^{6}-20iq^{7}+\cdots$$
1150.4.b.c $2$ $67.852$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}+4iq^{3}-4q^{4}-8q^{6}-3iq^{7}+\cdots$$
1150.4.b.d $2$ $67.852$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}+iq^{3}-4q^{4}-2q^{6}-2^{5}iq^{7}+\cdots$$
1150.4.b.e $2$ $67.852$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2iq^{2}+iq^{3}-4q^{4}+2q^{6}-12iq^{7}+\cdots$$
1150.4.b.f $2$ $67.852$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2iq^{2}+iq^{3}-4q^{4}+2q^{6}+18iq^{7}+\cdots$$
1150.4.b.g $2$ $67.852$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2iq^{2}+2iq^{3}-4q^{4}+4q^{6}-21iq^{7}+\cdots$$
1150.4.b.h $2$ $67.852$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2iq^{2}+5iq^{3}-4q^{4}+10q^{6}+12iq^{7}+\cdots$$
1150.4.b.i $4$ $67.852$ $$\Q(i, \sqrt{41})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2\beta _{2}q^{2}+(-3\beta _{1}-\beta _{2})q^{3}-4q^{4}+\cdots$$
1150.4.b.j $4$ $67.852$ $$\Q(i, \sqrt{73})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(4+\cdots)q^{6}+\cdots$$
1150.4.b.k $4$ $67.852$ $$\Q(i, \sqrt{73})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(4+\cdots)q^{6}+\cdots$$
1150.4.b.l $6$ $67.852$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{2}q^{2}+\beta _{1}q^{3}-4q^{4}-2\beta _{3}q^{6}+\cdots$$
1150.4.b.m $8$ $67.852$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(2+\cdots)q^{6}+\cdots$$
1150.4.b.n $8$ $67.852$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(2+\cdots)q^{6}+\cdots$$
1150.4.b.o $8$ $67.852$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{6}q^{2}+(\beta _{1}-3\beta _{6})q^{3}-4q^{4}+(6+\cdots)q^{6}+\cdots$$
1150.4.b.p $10$ $67.852$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2\beta _{5}q^{2}+(-2\beta _{5}+\beta _{8})q^{3}-4q^{4}+\cdots$$
1150.4.b.q $10$ $67.852$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2\beta _{6}q^{2}+\beta _{1}q^{3}-4q^{4}+2\beta _{2}q^{6}+\cdots$$
1150.4.b.r $10$ $67.852$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(2+\cdots)q^{6}+\cdots$$
1150.4.b.s $12$ $67.852$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{7}q^{2}+(\beta _{1}+\beta _{7})q^{3}-4q^{4}+(-2+\cdots)q^{6}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(1150, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(1150, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(10, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(115, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(230, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(575, [\chi])$$$$^{\oplus 2}$$