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Properties

Label 950.6.r
Level $950$
Weight $6$
Character orbit 950.r
Rep. character $\chi_{950}(11,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $2000$
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.r (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(900\)

Dimensions

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

Total New Old
Modular forms 6032 2000 4032
Cusp forms 5968 2000 3968
Eisenstein series 64 0 64

Trace form

\( 2000 q + 4000 q^{4} + 22 q^{5} + 472 q^{7} + 20250 q^{9} + O(q^{10}) \) \( 2000 q + 4000 q^{4} + 22 q^{5} + 472 q^{7} + 20250 q^{9} - 948 q^{11} + 2096 q^{13} + 1568 q^{14} + 286 q^{15} + 64000 q^{16} - 78 q^{17} + 9088 q^{18} + 5268 q^{19} - 704 q^{20} - 8688 q^{21} + 2832 q^{22} + 12718 q^{23} - 7010 q^{25} + 30204 q^{27} - 3776 q^{28} + 1584 q^{29} + 33968 q^{30} - 1560 q^{33} + 9248 q^{34} - 20980 q^{35} + 324000 q^{36} - 26224 q^{37} - 17360 q^{38} + 4296 q^{39} + 26896 q^{41} + 40832 q^{42} - 53220 q^{43} - 5056 q^{44} - 237512 q^{45} - 114688 q^{46} - 13564 q^{47} + 4827960 q^{49} + 43232 q^{50} - 71252 q^{51} + 33536 q^{52} + 11124 q^{53} + 39408 q^{54} + 68280 q^{55} - 50176 q^{56} - 257052 q^{57} - 16512 q^{59} - 14944 q^{60} + 47188 q^{61} + 31712 q^{62} + 774 q^{63} - 2048000 q^{64} - 822864 q^{65} + 87104 q^{66} + 132088 q^{67} + 112256 q^{68} - 11376 q^{69} - 22816 q^{70} + 58774 q^{71} - 72704 q^{72} - 160280 q^{73} - 983280 q^{75} - 56192 q^{76} - 666768 q^{77} - 27920 q^{78} - 28328 q^{79} + 5632 q^{80} + 1790434 q^{81} + 63712 q^{82} + 221864 q^{83} - 699264 q^{84} + 125230 q^{85} + 147920 q^{86} + 377584 q^{87} + 60416 q^{88} + 167652 q^{89} - 664584 q^{90} + 66248 q^{91} - 205952 q^{92} - 401252 q^{93} - 582400 q^{94} - 226352 q^{95} + 303022 q^{97} + 114176 q^{98} - 224012 q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)