# Properties

 Label 150.6.h Level $150$ Weight $6$ Character orbit 150.h Rep. character $\chi_{150}(19,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $104$ Sturm bound $180$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$150 = 2 \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 150.h (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$25$$ Character field: $$\Q(\zeta_{10})$$ Sturm bound: $$180$$

## Dimensions

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

Total New Old
Modular forms 616 104 512
Cusp forms 584 104 480
Eisenstein series 32 0 32

## Trace form

 $$104q + 416q^{4} + 104q^{5} - 72q^{6} + 2106q^{9} + O(q^{10})$$ $$104q + 416q^{4} + 104q^{5} - 72q^{6} + 2106q^{9} + 72q^{10} - 948q^{11} + 198q^{15} - 6656q^{16} - 3820q^{17} + 6712q^{19} + 3136q^{20} - 1764q^{21} - 4720q^{22} - 24820q^{23} - 4608q^{24} - 8846q^{25} - 1952q^{26} + 3040q^{28} + 24248q^{29} + 16704q^{30} + 9966q^{31} + 7380q^{33} - 11920q^{34} - 25944q^{35} - 33696q^{36} - 25900q^{37} - 1152q^{40} - 47396q^{41} + 43560q^{42} - 10112q^{44} - 8424q^{45} - 37136q^{46} - 66440q^{47} - 340924q^{49} + 21152q^{50} + 41616q^{51} - 44700q^{53} + 5832q^{54} + 118988q^{55} + 93600q^{59} - 19008q^{60} - 165308q^{61} + 186960q^{62} - 95580q^{63} + 106496q^{64} + 36912q^{65} - 34848q^{66} + 118360q^{67} + 108576q^{69} - 63192q^{70} - 161128q^{71} - 121200q^{73} - 124832q^{74} - 87192q^{75} + 148608q^{76} - 239120q^{77} + 4236q^{79} + 26624q^{80} - 170586q^{81} + 224840q^{83} + 28224q^{84} - 242684q^{85} + 201696q^{86} + 185580q^{87} + 56960q^{88} + 147816q^{89} - 5832q^{90} + 213428q^{91} - 8448q^{94} + 216000q^{95} - 18432q^{96} + 329650q^{97} + 412480q^{98} - 51192q^{99} + O(q^{100})$$

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

The newforms in this space have not yet been added to the LMFDB.

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

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