# Properties

 Label 150.6.g Level $150$ Weight $6$ Character orbit 150.g Rep. character $\chi_{150}(31,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $96$ Newform subspaces $4$ Sturm bound $180$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$150 = 2 \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 150.g (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$25$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$4$$ Sturm bound: $$180$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(150, [\chi])$$.

Total New Old
Modular forms 616 96 520
Cusp forms 584 96 488
Eisenstein series 32 0 32

## Trace form

 $$96q - 8q^{2} - 384q^{4} + 66q^{5} + 72q^{6} - 548q^{7} - 128q^{8} - 1944q^{9} + O(q^{10})$$ $$96q - 8q^{2} - 384q^{4} + 66q^{5} + 72q^{6} - 548q^{7} - 128q^{8} - 1944q^{9} + 64q^{10} + 948q^{11} + 772q^{13} - 594q^{15} - 6144q^{16} + 152q^{17} + 2592q^{18} + 6712q^{19} - 704q^{20} + 1764q^{21} - 1408q^{22} - 7236q^{23} - 4608q^{24} + 13624q^{25} + 9552q^{26} - 5728q^{28} + 18348q^{29} + 16704q^{30} - 9966q^{31} + 8192q^{32} - 288q^{33} + 24680q^{34} - 48304q^{35} - 31104q^{36} - 23474q^{37} - 1984q^{38} + 1024q^{40} + 5496q^{41} - 26136q^{42} + 84128q^{43} - 10112q^{44} + 5346q^{45} + 37136q^{46} - 39512q^{47} + 139276q^{49} + 7576q^{50} - 41616q^{51} + 12352q^{52} + 62310q^{53} + 5832q^{54} - 18760q^{55} + 23544q^{57} - 10176q^{58} + 93600q^{59} + 6336q^{60} + 127408q^{61} - 175600q^{62} + 51192q^{63} - 98304q^{64} - 138638q^{65} + 34848q^{66} + 184352q^{67} + 63552q^{68} + 108576q^{69} - 536q^{70} + 161128q^{71} - 10368q^{72} - 334848q^{73} - 117232q^{74} - 28296q^{75} - 148608q^{76} + 141776q^{77} - 16704q^{78} + 4236q^{79} + 16896q^{80} - 157464q^{81} + 263216q^{82} - 605608q^{83} + 28224q^{84} + 861566q^{85} - 201696q^{86} + 350496q^{87} - 3968q^{88} - 5334q^{89} + 5184q^{90} - 213428q^{91} + 77184q^{92} - 115056q^{93} - 8448q^{94} - 497584q^{95} + 18432q^{96} - 787294q^{97} - 422344q^{98} - 51192q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(150, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
150.6.g.a $$20$$ $$24.058$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$20$$ $$45$$ $$-55$$ $$180$$ $$q-4\beta _{6}q^{2}-9\beta _{7}q^{3}+2^{4}\beta _{7}q^{4}+(-5+\cdots)q^{5}+\cdots$$
150.6.g.b $$24$$ $$24.058$$ None $$-24$$ $$-54$$ $$30$$ $$-212$$
150.6.g.c $$24$$ $$24.058$$ None $$24$$ $$-54$$ $$80$$ $$-454$$
150.6.g.d $$28$$ $$24.058$$ None $$-28$$ $$63$$ $$11$$ $$-62$$

## Decomposition of $$S_{6}^{\mathrm{old}}(150, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(150, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 2}$$