# Properties

 Label 2340.2.q Level $2340$ Weight $2$ Character orbit 2340.q Rep. character $\chi_{2340}(1621,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $48$ Newform subspaces $11$ Sturm bound $1008$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2340.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$11$$ Sturm bound: $$1008$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2340, [\chi])$$.

Total New Old
Modular forms 1056 48 1008
Cusp forms 960 48 912
Eisenstein series 96 0 96

## Trace form

 $$48 q - 2 q^{7} + O(q^{10})$$ $$48 q - 2 q^{7} + 4 q^{11} - 2 q^{17} - 4 q^{19} - 2 q^{23} + 48 q^{25} - 4 q^{29} - 24 q^{31} - 6 q^{35} - 6 q^{37} - 4 q^{41} + 6 q^{43} - 56 q^{47} - 24 q^{49} + 8 q^{53} + 8 q^{55} - 8 q^{59} + 20 q^{61} + 8 q^{65} + 22 q^{67} + 24 q^{71} - 32 q^{73} - 12 q^{77} - 32 q^{79} + 48 q^{83} + 6 q^{85} + 32 q^{89} - 12 q^{91} + 18 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2340, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2340.2.q.a $2$ $18.685$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$-3$$ $$q-q^{5}-3\zeta_{6}q^{7}+(3-3\zeta_{6})q^{11}+(-1+\cdots)q^{13}+\cdots$$
2340.2.q.b $2$ $18.685$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$1$$ $$q-q^{5}+\zeta_{6}q^{7}+(3-3\zeta_{6})q^{11}+(3-4\zeta_{6})q^{13}+\cdots$$
2340.2.q.c $2$ $18.685$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$-5$$ $$q+q^{5}-5\zeta_{6}q^{7}+(-5+5\zeta_{6})q^{11}+\cdots$$
2340.2.q.d $2$ $18.685$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$-3$$ $$q+q^{5}-3\zeta_{6}q^{7}+(6-6\zeta_{6})q^{11}+(-4+\cdots)q^{13}+\cdots$$
2340.2.q.e $2$ $18.685$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$1$$ $$q+q^{5}+\zeta_{6}q^{7}+(-2+2\zeta_{6})q^{11}+(4+\cdots)q^{13}+\cdots$$
2340.2.q.f $2$ $18.685$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$1$$ $$q+q^{5}+\zeta_{6}q^{7}+(3-3\zeta_{6})q^{11}+(-1+\cdots)q^{13}+\cdots$$
2340.2.q.g $4$ $18.685$ $$\Q(\sqrt{-3}, \sqrt{10})$$ None $$0$$ $$0$$ $$-4$$ $$2$$ $$q-q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+2\beta _{2}q^{11}+\cdots$$
2340.2.q.h $6$ $18.685$ 6.0.31259952.1 None $$0$$ $$0$$ $$-6$$ $$1$$ $$q-q^{5}+(-\beta _{4}+\beta _{5})q^{7}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots$$
2340.2.q.i $6$ $18.685$ 6.0.16765488.1 None $$0$$ $$0$$ $$6$$ $$1$$ $$q+q^{5}+(\beta _{1}-\beta _{5})q^{7}+(1+\beta _{2})q^{13}+\cdots$$
2340.2.q.j $10$ $18.685$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$0$$ $$-10$$ $$1$$ $$q-q^{5}+\beta _{8}q^{7}+(-1+\beta _{1}-\beta _{7}+\beta _{9})q^{11}+\cdots$$
2340.2.q.k $10$ $18.685$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$0$$ $$0$$ $$10$$ $$1$$ $$q+q^{5}+\beta _{8}q^{7}+(1-\beta _{1}+\beta _{7}-\beta _{9})q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2340, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2340, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(117, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(130, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(156, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(234, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(260, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(390, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(468, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(585, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(780, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1170, [\chi])$$$$^{\oplus 2}$$