# Properties

 Label 1183.2.e Level $1183$ Weight $2$ Character orbit 1183.e Rep. character $\chi_{1183}(170,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $184$ Newform subspaces $12$ Sturm bound $242$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1183 = 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1183.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$12$$ Sturm bound: $$242$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1183, [\chi])$$.

Total New Old
Modular forms 272 228 44
Cusp forms 216 184 32
Eisenstein series 56 44 12

## Trace form

 $$184 q + 2 q^{2} - 78 q^{4} + 2 q^{5} + 6 q^{7} - 72 q^{9} + O(q^{10})$$ $$184 q + 2 q^{2} - 78 q^{4} + 2 q^{5} + 6 q^{7} - 72 q^{9} - 10 q^{10} + 2 q^{11} - 10 q^{12} - 16 q^{14} + 20 q^{15} - 42 q^{16} - 2 q^{17} + 8 q^{19} - 32 q^{20} - 2 q^{21} - 32 q^{22} - 10 q^{23} + 20 q^{24} - 50 q^{25} - 60 q^{27} - 30 q^{28} + 16 q^{29} - 16 q^{30} + 4 q^{31} + 12 q^{32} + 8 q^{33} + 32 q^{34} + 16 q^{35} + 28 q^{36} + 8 q^{37} - 14 q^{38} - 4 q^{40} - 28 q^{41} - 30 q^{42} + 28 q^{43} - 6 q^{44} - 32 q^{45} + 20 q^{46} + 2 q^{47} + 188 q^{48} + 26 q^{49} - 8 q^{50} - 18 q^{51} + 18 q^{54} - 8 q^{55} + 8 q^{56} + 32 q^{57} - 42 q^{58} + 10 q^{59} - 44 q^{60} - 14 q^{61} + 72 q^{62} - 40 q^{63} - 8 q^{64} + 4 q^{66} + 4 q^{67} + 84 q^{68} - 64 q^{69} - 54 q^{70} - 20 q^{71} - 22 q^{72} + 22 q^{73} - 34 q^{74} - 24 q^{75} - 48 q^{76} + 36 q^{77} - 6 q^{79} + 70 q^{80} - 28 q^{81} + 20 q^{82} - 12 q^{83} + 98 q^{84} + 4 q^{85} + 54 q^{86} - 80 q^{87} + 30 q^{88} - 4 q^{89} + 196 q^{90} - 40 q^{92} + 18 q^{93} + 48 q^{94} - 14 q^{95} - 22 q^{96} + 68 q^{97} - 34 q^{98} - 16 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1183, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1183.2.e.a $2$ $9.446$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$3$$ $$-3$$ $$1$$ $$q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$$
1183.2.e.b $2$ $9.446$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$0$$ $$-1$$ $$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(-2+3\zeta_{6})q^{7}+\cdots$$
1183.2.e.c $2$ $9.446$ $$\Q(\sqrt{-3})$$ None $$1$$ $$3$$ $$3$$ $$-1$$ $$q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$$
1183.2.e.d $4$ $9.446$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None $$-3$$ $$0$$ $$0$$ $$8$$ $$q+(-1-\beta _{1}-\beta _{3})q^{2}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{3}+\cdots$$
1183.2.e.e $4$ $9.446$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{3}+\cdots$$
1183.2.e.f $10$ $9.446$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$4$$ $$0$$ $$2$$ $$-1$$ $$q+(-\beta _{1}+\beta _{7})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+\cdots$$
1183.2.e.g $12$ $9.446$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-2$$ $$1$$ $$-1$$ $$6$$ $$q+(\beta _{1}+\beta _{5}-\beta _{11})q^{2}-\beta _{3}q^{3}+(\beta _{6}+\cdots)q^{4}+\cdots$$
1183.2.e.h $12$ $9.446$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$2$$ $$1$$ $$1$$ $$-6$$ $$q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}-\beta _{3}q^{3}+(\beta _{6}+\cdots)q^{4}+\cdots$$
1183.2.e.i $16$ $9.446$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{9}q^{2}+(-1-\beta _{4}-\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots$$
1183.2.e.j $24$ $9.446$ None $$0$$ $$-6$$ $$0$$ $$0$$
1183.2.e.k $48$ $9.446$ None $$-1$$ $$0$$ $$13$$ $$-3$$
1183.2.e.l $48$ $9.446$ None $$1$$ $$0$$ $$-13$$ $$3$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1183, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1183, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 2}$$