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

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

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

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