Properties

 Label 1092.2.e Level $1092$ Weight $2$ Character orbit 1092.e Rep. character $\chi_{1092}(337,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $5$ Sturm bound $448$ Trace bound $17$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1092 = 2^{2} \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1092.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$448$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1092, [\chi])$$.

Total New Old
Modular forms 236 12 224
Cusp forms 212 12 200
Eisenstein series 24 0 24

Trace form

 $$12 q + 12 q^{9} + O(q^{10})$$ $$12 q + 12 q^{9} - 8 q^{13} - 8 q^{17} + 28 q^{23} - 8 q^{25} + 12 q^{29} - 4 q^{35} - 8 q^{39} + 12 q^{43} - 12 q^{49} + 16 q^{51} - 20 q^{53} + 32 q^{55} - 32 q^{61} + 12 q^{65} + 8 q^{69} - 16 q^{77} + 52 q^{79} + 12 q^{81} - 8 q^{87} + 4 q^{91} - 12 q^{95} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(1092, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1092.2.e.a $2$ $8.720$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+2iq^{5}+iq^{7}+q^{9}+2iq^{11}+\cdots$$
1092.2.e.b $2$ $8.720$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+4iq^{5}+iq^{7}+q^{9}+(-3+2i)q^{13}+\cdots$$
1092.2.e.c $2$ $8.720$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+iq^{7}+q^{9}+4iq^{11}+(-3+\cdots)q^{13}+\cdots$$
1092.2.e.d $2$ $8.720$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+iq^{5}-iq^{7}+q^{9}+(2+3i)q^{13}+\cdots$$
1092.2.e.e $4$ $8.720$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(1092, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1092, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(156, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(364, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(546, [\chi])$$$$^{\oplus 2}$$