Properties

Label 950.6.h
Level $950$
Weight $6$
Character orbit 950.h
Rep. character $\chi_{950}(191,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $896$
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.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(900\)

Dimensions

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

Total New Old
Modular forms 3016 896 2120
Cusp forms 2984 896 2088
Eisenstein series 32 0 32

Trace form

\( 896 q - 8 q^{2} + 8 q^{3} - 3584 q^{4} + 508 q^{5} + 144 q^{6} - 388 q^{7} - 128 q^{8} - 17572 q^{9} + O(q^{10}) \) \( 896 q - 8 q^{2} + 8 q^{3} - 3584 q^{4} + 508 q^{5} + 144 q^{6} - 388 q^{7} - 128 q^{8} - 17572 q^{9} - 200 q^{10} + 958 q^{11} - 192 q^{12} - 1868 q^{13} + 332 q^{15} - 57344 q^{16} + 1298 q^{17} + 12960 q^{18} + 722 q^{19} - 2912 q^{20} + 2848 q^{22} + 13922 q^{23} - 9216 q^{24} - 24036 q^{25} - 22896 q^{26} + 4316 q^{27} - 128 q^{28} + 1332 q^{29} - 3408 q^{30} - 37668 q^{31} + 8192 q^{32} - 38884 q^{33} + 3960 q^{34} - 22522 q^{35} - 281152 q^{36} - 61710 q^{37} - 31160 q^{39} - 3200 q^{40} + 5496 q^{41} - 105168 q^{42} + 34420 q^{43} + 2688 q^{44} - 17060 q^{45} - 6284 q^{47} - 3072 q^{48} + 2043092 q^{49} + 28760 q^{50} - 64776 q^{51} - 29888 q^{52} - 197562 q^{53} + 46656 q^{54} - 25024 q^{55} + 74640 q^{58} - 171372 q^{59} - 97728 q^{60} + 32596 q^{61} - 32832 q^{62} + 561398 q^{63} - 917504 q^{64} - 95206 q^{65} + 69696 q^{66} + 151516 q^{67} + 51328 q^{68} - 338536 q^{69} + 219808 q^{70} + 128200 q^{71} - 51840 q^{72} - 223848 q^{73} - 555312 q^{74} + 543980 q^{75} - 46208 q^{76} - 112544 q^{77} - 155760 q^{78} - 283856 q^{79} - 18432 q^{80} - 1572884 q^{81} + 889968 q^{82} + 481150 q^{83} + 901944 q^{85} - 201696 q^{86} + 478296 q^{87} - 68352 q^{88} - 244298 q^{89} - 356680 q^{90} - 498896 q^{91} - 308608 q^{92} - 2107696 q^{93} + 72922 q^{95} + 36864 q^{96} - 420800 q^{97} - 172872 q^{98} - 1454188 q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)