↑

Properties

Label 950.6.x
Level $950$
Weight $6$
Character orbit 950.x
Rep. character $\chi_{950}(159,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $2000$
Sturm bound $900$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 950.x (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 2000 q - 4000 q^{4} + 22 q^{5} - 20250 q^{9} + O(q^{10}) \) \( 2000 q - 4000 q^{4} + 22 q^{5} - 20250 q^{9} + 948 q^{11} + 1568 q^{14} - 2458 q^{15} + 64000 q^{16} - 1910 q^{17} + 5268 q^{19} + 704 q^{20} + 8688 q^{21} + 4720 q^{22} + 6030 q^{23} + 14006 q^{25} - 50340 q^{27} + 1584 q^{29} + 32848 q^{30} - 7380 q^{33} + 9248 q^{34} - 20968 q^{35} + 324000 q^{36} + 4296 q^{39} - 26896 q^{41} - 5056 q^{44} + 281776 q^{45} + 114688 q^{46} + 135320 q^{47} - 4776040 q^{49} + 65120 q^{50} + 71252 q^{51} - 71560 q^{53} + 39408 q^{54} - 15568 q^{55} + 50176 q^{56} - 16512 q^{59} + 19808 q^{60} - 47188 q^{61} - 452590 q^{63} + 2048000 q^{64} - 675008 q^{65} - 87104 q^{66} + 236720 q^{67} - 11376 q^{69} + 5568 q^{70} - 58774 q^{71} + 166480 q^{73} - 870984 q^{75} + 56192 q^{76} - 868080 q^{77} - 81840 q^{78} - 28328 q^{79} + 5632 q^{80} + 1490066 q^{81} + 572080 q^{83} - 699264 q^{84} - 473562 q^{85} - 147920 q^{86} + 709680 q^{87} + 167652 q^{89} + 686328 q^{90} - 66248 q^{91} + 210880 q^{92} - 582400 q^{94} - 94396 q^{95} - 206130 q^{97} - 206240 q^{98} - 224012 q^{99} + O(q^{100}) \)

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

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