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Properties

Label 950.6.l
Level $950$
Weight $6$
Character orbit 950.l
Rep. character $\chi_{950}(101,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $954$
Sturm bound $900$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 950.l (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(900\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(950, [\chi])\).

Total New Old
Modular forms 4572 954 3618
Cusp forms 4428 954 3474
Eisenstein series 144 0 144

Trace form

\( 954 q + 33 q^{3} - 12 q^{6} - 354 q^{7} - 192 q^{8} + 33 q^{9} + O(q^{10}) \) \( 954 q + 33 q^{3} - 12 q^{6} - 354 q^{7} - 192 q^{8} + 33 q^{9} - 474 q^{11} - 4272 q^{13} + 2640 q^{14} + 2892 q^{17} - 984 q^{18} + 14490 q^{19} - 5076 q^{21} + 720 q^{22} - 9228 q^{23} - 192 q^{24} + 1320 q^{26} + 7887 q^{27} + 6816 q^{28} - 18582 q^{29} - 6546 q^{31} + 14307 q^{33} - 9168 q^{34} + 528 q^{36} + 20052 q^{37} - 6756 q^{38} + 105924 q^{39} + 11211 q^{41} + 17712 q^{42} + 109986 q^{43} + 22464 q^{44} + 45600 q^{46} - 96930 q^{47} - 16896 q^{48} - 1181745 q^{49} - 35961 q^{51} + 3936 q^{52} + 104616 q^{53} + 20196 q^{54} - 83712 q^{56} + 59244 q^{57} + 64416 q^{58} + 13863 q^{59} - 81750 q^{61} - 138408 q^{62} - 314952 q^{63} - 1953792 q^{64} + 511812 q^{66} - 47421 q^{67} + 6288 q^{68} + 84366 q^{69} - 197562 q^{71} + 92544 q^{72} + 201390 q^{73} + 111240 q^{74} - 37920 q^{76} - 537708 q^{77} - 174552 q^{78} - 116610 q^{79} + 409947 q^{81} + 71052 q^{82} + 63666 q^{83} + 231264 q^{84} + 107712 q^{86} + 299682 q^{87} - 46464 q^{88} + 103632 q^{89} - 399360 q^{91} - 248736 q^{92} - 613806 q^{93} - 149328 q^{94} - 282933 q^{97} - 337440 q^{98} - 411327 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(950, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(950, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)