# Properties

 Label 354.3.h Level 354 Weight 3 Character orbit h Rep. character $$\chi_{354}(5,\cdot)$$ Character field $$\Q(\zeta_{58})$$ Dimension 1120 Newform subspaces 1 Sturm bound 180 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$354 = 2 \cdot 3 \cdot 59$$ Weight: $$k$$ = $$3$$ Character orbit: $$[\chi]$$ = 354.h (of order $$58$$ and degree $$28$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$177$$ Character field: $$\Q(\zeta_{58})$$ Newform subspaces: $$1$$ Sturm bound: $$180$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(354, [\chi])$$.

Total New Old
Modular forms 3472 1120 2352
Cusp forms 3248 1120 2128
Eisenstein series 224 0 224

## Trace form

 $$1120q + 80q^{4} - 8q^{6} - 8q^{7} + 24q^{9} + O(q^{10})$$ $$1120q + 80q^{4} - 8q^{6} - 8q^{7} + 24q^{9} + 16q^{10} - 34q^{15} - 160q^{16} - 16q^{18} - 24q^{19} + 18q^{21} + 16q^{22} + 16q^{24} + 216q^{25} + 30q^{27} + 16q^{28} + 64q^{30} - 96q^{31} - 76q^{33} - 80q^{34} - 48q^{36} + 200q^{37} + 28q^{39} - 32q^{40} - 48q^{42} + 104q^{43} + 696q^{45} - 32q^{46} - 288q^{49} + 1800q^{51} + 852q^{54} - 360q^{55} + 76q^{57} + 128q^{58} - 280q^{60} + 32q^{61} - 1318q^{63} + 320q^{64} - 1512q^{66} + 344q^{67} - 2640q^{69} - 192q^{70} + 32q^{72} - 40q^{73} - 1014q^{75} + 48q^{76} - 96q^{78} - 32q^{79} - 336q^{81} + 80q^{82} - 36q^{84} - 168q^{85} + 162q^{87} - 32q^{88} - 112q^{90} - 88q^{91} + 316q^{93} + 400q^{94} - 32q^{96} + 184q^{97} + 148q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(354, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
354.3.h.a $$1120$$ $$9.646$$ None $$0$$ $$0$$ $$0$$ $$-8$$

## Decomposition of $$S_{3}^{\mathrm{old}}(354, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(354, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(177, [\chi])$$$$^{\oplus 2}$$