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Properties

Label 950.6
Level 950
Weight 6
Dimension 41245
Nonzero newspaces 18
Sturm bound 324000
Trace bound 7

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Defining parameters

Level: \( N \) = \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(324000\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(950))\).

Total New Old
Modular forms 136008 41245 94763
Cusp forms 133992 41245 92747
Eisenstein series 2016 0 2016

Trace form

\( 41245q - 16q^{2} + 16q^{3} + 64q^{4} + 170q^{5} - 320q^{6} - 1248q^{7} - 256q^{8} + 2612q^{9} + O(q^{10}) \) \( 41245q - 16q^{2} + 16q^{3} + 64q^{4} + 170q^{5} - 320q^{6} - 1248q^{7} - 256q^{8} + 2612q^{9} - 360q^{10} - 2960q^{11} + 1120q^{12} - 3888q^{13} + 2312q^{14} + 1640q^{15} + 5120q^{16} + 334q^{17} + 9380q^{18} + 19210q^{19} - 1280q^{20} + 2350q^{21} - 14164q^{22} - 34582q^{23} - 13824q^{24} - 50670q^{25} - 7480q^{26} + 9517q^{27} + 6496q^{28} + 57482q^{29} + 60000q^{30} + 25402q^{31} + 6144q^{32} + 113766q^{33} + 27432q^{34} - 121720q^{35} + 29760q^{36} - 104176q^{37} - 34720q^{38} - 64050q^{39} - 640q^{40} + 73682q^{41} + 45568q^{42} + 170266q^{43} + 23504q^{44} - 3670q^{45} - 20944q^{46} - 132280q^{47} - 21248q^{48} - 372462q^{49} - 22600q^{50} - 8209q^{51} + 10080q^{52} - 119466q^{53} - 5304q^{54} + 132360q^{55} + 51456q^{56} + 498950q^{57} + 245904q^{58} + 266930q^{59} - 225280q^{60} - 300634q^{61} + 97384q^{62} - 13400q^{63} - 8192q^{64} + 675730q^{65} - 171008q^{66} + 144526q^{67} + 193488q^{68} + 577050q^{69} - 94720q^{70} + 257456q^{71} - 110272q^{72} - 582407q^{73} - 1141248q^{74} - 1784920q^{75} - 89600q^{76} - 4140464q^{77} - 3021328q^{78} - 1536962q^{79} + 43520q^{80} + 3193043q^{81} + 2744176q^{82} + 3813480q^{83} + 3499680q^{84} + 3647282q^{85} + 1985520q^{86} + 5781148q^{87} + 211968q^{88} + 203602q^{89} - 1941000q^{90} - 2509184q^{91} - 2618176q^{92} - 9348842q^{93} - 5086432q^{94} - 2267596q^{95} - 81920q^{96} - 3810242q^{97} - 2588016q^{98} - 6199789q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(950))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
950.6.a \(\chi_{950}(1, \cdot)\) 950.6.a.a 1 1
950.6.a.b 1
950.6.a.c 1
950.6.a.d 2
950.6.a.e 2
950.6.a.f 3
950.6.a.g 3
950.6.a.h 3
950.6.a.i 3
950.6.a.j 4
950.6.a.k 4
950.6.a.l 5
950.6.a.m 5
950.6.a.n 6
950.6.a.o 6
950.6.a.p 6
950.6.a.q 6
950.6.a.r 9
950.6.a.s 9
950.6.a.t 9
950.6.a.u 9
950.6.a.v 11
950.6.a.w 11
950.6.a.x 12
950.6.a.y 12
950.6.b \(\chi_{950}(799, \cdot)\) n/a 134 1
950.6.e \(\chi_{950}(201, \cdot)\) n/a 314 2
950.6.f \(\chi_{950}(493, \cdot)\) n/a 300 2
950.6.h \(\chi_{950}(191, \cdot)\) n/a 896 4
950.6.j \(\chi_{950}(49, \cdot)\) n/a 300 2
950.6.l \(\chi_{950}(101, \cdot)\) n/a 954 6
950.6.n \(\chi_{950}(39, \cdot)\) n/a 904 4
950.6.q \(\chi_{950}(107, \cdot)\) n/a 600 4
950.6.r \(\chi_{950}(11, \cdot)\) n/a 2000 8
950.6.u \(\chi_{950}(99, \cdot)\) n/a 900 6
950.6.w \(\chi_{950}(37, \cdot)\) n/a 2000 8
950.6.x \(\chi_{950}(159, \cdot)\) n/a 2000 8
950.6.bb \(\chi_{950}(143, \cdot)\) n/a 1800 12
950.6.bc \(\chi_{950}(61, \cdot)\) n/a 6000 24
950.6.bd \(\chi_{950}(27, \cdot)\) n/a 4000 16
950.6.bg \(\chi_{950}(9, \cdot)\) n/a 6000 24
950.6.bi \(\chi_{950}(3, \cdot)\) n/a 12000 48

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(950))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(950)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(475))\)\(^{\oplus 2}\)