Properties

Label 150.6
Level 150
Weight 6
Dimension 691
Nonzero newspaces 6
Sturm bound 7200
Trace bound 1

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Defining parameters

Level: \( N \) = \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(7200\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(150))\).

Total New Old
Modular forms 3112 691 2421
Cusp forms 2888 691 2197
Eisenstein series 224 0 224

Trace form

\( 691q - 12q^{2} - q^{3} + 80q^{4} + 170q^{5} - 196q^{6} - 1072q^{7} - 192q^{8} + 405q^{9} + O(q^{10}) \) \( 691q - 12q^{2} - q^{3} + 80q^{4} + 170q^{5} - 196q^{6} - 1072q^{7} - 192q^{8} + 405q^{9} + 632q^{10} + 20q^{11} - 272q^{12} - 4394q^{13} + 704q^{14} - 3524q^{15} + 5376q^{16} - 110q^{17} + 6812q^{18} + 27804q^{19} + 2432q^{20} + 296q^{21} - 11568q^{22} - 26632q^{23} - 7488q^{24} - 45566q^{25} - 6152q^{26} - 33841q^{27} - 4992q^{28} + 34046q^{29} + 30000q^{30} + 22088q^{31} + 7168q^{32} + 15332q^{33} - 4816q^{34} - 74248q^{35} + 1616q^{36} + 75396q^{37} - 144q^{38} + 13082q^{39} + 384q^{40} - 23766q^{41} - 65216q^{42} - 34396q^{43} - 41408q^{44} - 44670q^{45} - 109600q^{46} - 98704q^{47} - 4352q^{48} - 173037q^{49} + 28728q^{50} + 235666q^{51} + 98656q^{52} + 50844q^{53} + 20412q^{54} + 232456q^{55} - 45056q^{56} - 9084q^{57} - 74056q^{58} + 63220q^{59} + 102912q^{60} - 331170q^{61} + 8352q^{62} - 275332q^{63} + 20480q^{64} - 101726q^{65} + 11360q^{66} + 352652q^{67} + 120480q^{68} + 458444q^{69} + 135168q^{70} - 31800q^{71} - 88256q^{72} - 878094q^{73} - 517960q^{74} + 383124q^{75} - 85824q^{76} - 205248q^{77} + 300760q^{78} + 241912q^{79} + 43520q^{80} + 204261q^{81} + 341320q^{82} - 420764q^{83} - 401088q^{84} + 300754q^{85} + 96784q^{86} - 645834q^{87} + 116992q^{88} + 164432q^{89} + 399304q^{90} + 135952q^{91} + 163968q^{92} + 1171420q^{93} - 112512q^{94} - 281584q^{95} + 31744q^{96} - 172750q^{97} + 36948q^{98} - 209628q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(150))\)

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
150.6.a \(\chi_{150}(1, \cdot)\) 150.6.a.a 1 1
150.6.a.b 1
150.6.a.c 1
150.6.a.d 1
150.6.a.e 1
150.6.a.f 1
150.6.a.g 1
150.6.a.h 1
150.6.a.i 1
150.6.a.j 1
150.6.a.k 1
150.6.a.l 1
150.6.a.m 1
150.6.a.n 2
150.6.a.o 2
150.6.c \(\chi_{150}(49, \cdot)\) 150.6.c.a 2 1
150.6.c.b 2
150.6.c.c 2
150.6.c.d 2
150.6.c.e 2
150.6.c.f 2
150.6.c.g 2
150.6.e \(\chi_{150}(107, \cdot)\) 150.6.e.a 16 2
150.6.e.b 20
150.6.e.c 24
150.6.g \(\chi_{150}(31, \cdot)\) 150.6.g.a 20 4
150.6.g.b 24
150.6.g.c 24
150.6.g.d 28
150.6.h \(\chi_{150}(19, \cdot)\) n/a 104 4
150.6.l \(\chi_{150}(17, \cdot)\) n/a 400 8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(150))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(150)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)