# Properties

 Label 354.2.e Level 354 Weight 2 Character orbit e Rep. character $$\chi_{354}(7,\cdot)$$ Character field $$\Q(\zeta_{29})$$ Dimension 280 Newform subspaces 4 Sturm bound 120 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ = $$354 = 2 \cdot 3 \cdot 59$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 354.e (of order $$29$$ and degree $$28$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$59$$ Character field: $$\Q(\zeta_{29})$$ Newform subspaces: $$4$$ Sturm bound: $$120$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(354, [\chi])$$.

Total New Old
Modular forms 1792 280 1512
Cusp forms 1568 280 1288
Eisenstein series 224 0 224

## Trace form

 $$280q - 10q^{4} + 2q^{6} + 4q^{7} - 10q^{9} + O(q^{10})$$ $$280q - 10q^{4} + 2q^{6} + 4q^{7} - 10q^{9} + 8q^{10} + 16q^{11} + 12q^{13} + 16q^{14} + 4q^{15} - 10q^{16} + 24q^{17} + 16q^{19} + 12q^{22} + 32q^{23} + 2q^{24} + 10q^{25} + 8q^{26} + 4q^{28} + 48q^{29} + 4q^{30} + 36q^{31} + 8q^{33} + 24q^{34} + 56q^{35} - 10q^{36} + 20q^{37} + 32q^{38} + 8q^{39} + 8q^{40} + 40q^{41} + 16q^{42} + 44q^{43} + 16q^{44} - 84q^{46} - 84q^{47} - 166q^{49} - 216q^{50} + 24q^{51} - 104q^{52} - 152q^{53} + 2q^{54} - 276q^{55} + 16q^{56} + 16q^{57} - 92q^{58} - 172q^{59} + 4q^{60} - 164q^{61} - 68q^{62} + 4q^{63} - 10q^{64} - 228q^{65} + 8q^{66} - 132q^{67} - 92q^{68} + 40q^{69} - 160q^{70} - 120q^{71} - 68q^{74} + 32q^{75} + 16q^{76} + 128q^{77} + 24q^{78} + 108q^{79} - 10q^{81} + 32q^{82} + 104q^{83} + 120q^{85} + 64q^{86} + 36q^{87} + 12q^{88} + 64q^{89} + 8q^{90} + 112q^{91} + 32q^{92} + 20q^{93} + 56q^{94} + 104q^{95} + 2q^{96} + 108q^{97} + 64q^{98} + 16q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(354, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
354.2.e.a $$56$$ $$2.827$$ None $$-2$$ $$-2$$ $$4$$ $$9$$
354.2.e.b $$56$$ $$2.827$$ None $$2$$ $$2$$ $$-2$$ $$1$$
354.2.e.c $$84$$ $$2.827$$ None $$-3$$ $$3$$ $$0$$ $$1$$
354.2.e.d $$84$$ $$2.827$$ None $$3$$ $$-3$$ $$-2$$ $$-7$$

## Decomposition of $$S_{2}^{\mathrm{old}}(354, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(354, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(59, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(118, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(177, [\chi])$$$$^{\oplus 2}$$