# Properties

 Label 552.2.q Level $552$ Weight $2$ Character orbit 552.q Rep. character $\chi_{552}(25,\cdot)$ Character field $\Q(\zeta_{11})$ Dimension $120$ Newform subspaces $4$ Sturm bound $192$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$552 = 2^{3} \cdot 3 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 552.q (of order $$11$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$23$$ Character field: $$\Q(\zeta_{11})$$ Newform subspaces: $$4$$ Sturm bound: $$192$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(552, [\chi])$$.

Total New Old
Modular forms 1040 120 920
Cusp forms 880 120 760
Eisenstein series 160 0 160

## Trace form

 $$120q - 12q^{9} + O(q^{10})$$ $$120q - 12q^{9} - 8q^{11} + 4q^{19} - 4q^{21} + 8q^{23} - 20q^{25} - 16q^{31} - 4q^{33} + 44q^{35} + 24q^{37} + 36q^{39} + 60q^{41} + 32q^{43} + 96q^{47} + 4q^{49} + 48q^{51} + 36q^{53} + 76q^{55} + 32q^{57} + 44q^{59} - 20q^{61} + 12q^{67} - 4q^{69} + 8q^{71} - 24q^{73} - 16q^{75} - 116q^{79} - 12q^{81} - 100q^{83} - 100q^{85} + 24q^{87} - 84q^{89} - 280q^{91} + 16q^{93} - 224q^{95} - 148q^{97} - 8q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(552, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
552.2.q.a $$30$$ $$4.408$$ None $$0$$ $$-3$$ $$0$$ $$-2$$
552.2.q.b $$30$$ $$4.408$$ None $$0$$ $$-3$$ $$0$$ $$0$$
552.2.q.c $$30$$ $$4.408$$ None $$0$$ $$3$$ $$-2$$ $$-2$$
552.2.q.d $$30$$ $$4.408$$ None $$0$$ $$3$$ $$2$$ $$4$$

## Decomposition of $$S_{2}^{\mathrm{old}}(552, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(552, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(23, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(46, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(69, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(92, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(138, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(184, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(276, [\chi])$$$$^{\oplus 2}$$