# Properties

 Label 2366.2.d Level $2366$ Weight $2$ Character orbit 2366.d Rep. character $\chi_{2366}(337,\cdot)$ Character field $\Q$ Dimension $76$ Newform subspaces $18$ Sturm bound $728$ Trace bound $10$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2366 = 2 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2366.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$18$$ Sturm bound: $$728$$ Trace bound: $$10$$ Distinguishing $$T_p$$: $$3$$, $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2366, [\chi])$$.

Total New Old
Modular forms 392 76 316
Cusp forms 336 76 260
Eisenstein series 56 0 56

## Trace form

 $$76q - 76q^{4} + 64q^{9} + O(q^{10})$$ $$76q - 76q^{4} + 64q^{9} + 8q^{10} - 4q^{14} + 76q^{16} + 8q^{17} - 4q^{22} - 16q^{23} - 72q^{25} + 24q^{27} - 12q^{29} - 8q^{30} + 4q^{35} - 64q^{36} + 16q^{38} - 8q^{40} - 4q^{42} - 28q^{43} - 76q^{49} + 8q^{51} + 12q^{53} - 40q^{55} + 4q^{56} + 16q^{61} - 24q^{62} - 76q^{64} + 48q^{66} - 8q^{68} - 32q^{69} + 4q^{74} + 80q^{75} + 24q^{77} + 56q^{79} + 52q^{81} - 48q^{82} - 80q^{87} + 4q^{88} - 48q^{90} + 16q^{92} - 32q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2366, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2366.2.d.a $$2$$ $$18.893$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-iq^{2}-2q^{3}-q^{4}-3iq^{5}+2iq^{6}+\cdots$$
2366.2.d.b $$2$$ $$18.893$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-iq^{2}-2q^{3}-q^{4}+2iq^{6}-iq^{7}+\cdots$$
2366.2.d.c $$2$$ $$18.893$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-iq^{2}-2q^{3}-q^{4}+iq^{5}+2iq^{6}+\cdots$$
2366.2.d.d $$2$$ $$18.893$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}-2iq^{5}-iq^{7}+iq^{8}+\cdots$$
2366.2.d.e $$2$$ $$18.893$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+iq^{2}+q^{3}-q^{4}+iq^{6}-iq^{7}-iq^{8}+\cdots$$
2366.2.d.f $$2$$ $$18.893$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+iq^{2}+q^{3}-q^{4}-3iq^{5}+iq^{6}+\cdots$$
2366.2.d.g $$2$$ $$18.893$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+iq^{2}+q^{3}-q^{4}-4iq^{5}+iq^{6}+\cdots$$
2366.2.d.h $$2$$ $$18.893$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q-iq^{2}+3q^{3}-q^{4}-3iq^{5}-3iq^{6}+\cdots$$
2366.2.d.i $$2$$ $$18.893$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q-iq^{2}+3q^{3}-q^{4}-3iq^{6}-iq^{7}+\cdots$$
2366.2.d.j $$2$$ $$18.893$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q-iq^{2}+3q^{3}-q^{4}+4iq^{5}-3iq^{6}+\cdots$$
2366.2.d.k $$4$$ $$18.893$$ $$\Q(\zeta_{12})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}+(-1+\zeta_{12}^{3})q^{3}-q^{4}+\cdots$$
2366.2.d.l $$4$$ $$18.893$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-q^{4}+(2\zeta_{12}+\cdots)q^{5}+\cdots$$
2366.2.d.m $$6$$ $$18.893$$ 6.0.153664.1 None $$0$$ $$-10$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}+(-2+\beta _{4})q^{3}-q^{4}-2\beta _{3}q^{5}+\cdots$$
2366.2.d.n $$6$$ $$18.893$$ 6.0.153664.1 None $$0$$ $$-8$$ $$0$$ $$0$$ $$q+\beta _{5}q^{2}+(-1-\beta _{2})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
2366.2.d.o $$6$$ $$18.893$$ 6.0.153664.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+(-1+\beta _{2}+2\beta _{4})q^{3}-q^{4}+\cdots$$
2366.2.d.p $$6$$ $$18.893$$ 6.0.153664.1 None $$0$$ $$4$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+(1-\beta _{4})q^{3}-q^{4}+(2\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$$
2366.2.d.q $$12$$ $$18.893$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\beta _{8}q^{2}-\beta _{11}q^{3}-q^{4}+(-\beta _{2}-\beta _{9}+\cdots)q^{5}+\cdots$$
2366.2.d.r $$12$$ $$18.893$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q-\beta _{7}q^{2}+\beta _{2}q^{3}-q^{4}+(-\beta _{6}+\beta _{7}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2366, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2366, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(169, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(338, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1183, [\chi])$$$$^{\oplus 2}$$