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 $180$

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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

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