Properties

Label 333.2
Level 333
Weight 2
Dimension 3087
Nonzero newspaces 24
Newform subspaces 57
Sturm bound 16416
Trace bound 9

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Defining parameters

Level: \( N \) = \( 333 = 3^{2} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 57 \)
Sturm bound: \(16416\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(333))\).

Total New Old
Modular forms 4392 3401 991
Cusp forms 3817 3087 730
Eisenstein series 575 314 261

Trace form

\( 3087 q - 54 q^{2} - 72 q^{3} - 54 q^{4} - 54 q^{5} - 72 q^{6} - 54 q^{7} - 54 q^{8} - 72 q^{9} + O(q^{10}) \) \( 3087 q - 54 q^{2} - 72 q^{3} - 54 q^{4} - 54 q^{5} - 72 q^{6} - 54 q^{7} - 54 q^{8} - 72 q^{9} - 162 q^{10} - 54 q^{11} - 72 q^{12} - 54 q^{13} - 54 q^{14} - 72 q^{15} - 54 q^{16} - 54 q^{17} - 72 q^{18} - 162 q^{19} - 54 q^{20} - 72 q^{21} - 54 q^{22} - 54 q^{23} - 72 q^{24} - 54 q^{25} - 63 q^{26} - 72 q^{27} - 222 q^{28} - 72 q^{29} - 72 q^{30} - 108 q^{31} - 126 q^{32} - 72 q^{33} - 126 q^{34} - 108 q^{35} - 72 q^{36} - 204 q^{37} - 144 q^{38} - 72 q^{39} - 189 q^{40} - 108 q^{41} - 72 q^{42} - 90 q^{43} - 126 q^{44} - 72 q^{45} - 234 q^{46} - 72 q^{47} - 72 q^{48} - 78 q^{49} - 63 q^{50} - 72 q^{51} - 54 q^{52} - 54 q^{53} - 72 q^{54} - 162 q^{55} - 54 q^{56} - 72 q^{57} - 72 q^{58} - 90 q^{59} - 72 q^{60} - 99 q^{61} - 144 q^{62} - 72 q^{63} - 288 q^{64} - 135 q^{65} - 72 q^{66} - 90 q^{67} - 162 q^{68} - 72 q^{69} - 252 q^{70} - 126 q^{71} - 252 q^{73} - 198 q^{74} - 144 q^{75} - 234 q^{76} - 126 q^{77} - 72 q^{78} - 126 q^{79} - 252 q^{80} - 72 q^{81} - 270 q^{82} - 90 q^{83} - 72 q^{84} - 135 q^{85} - 180 q^{86} - 72 q^{87} - 144 q^{88} - 99 q^{89} - 72 q^{90} - 180 q^{91} + 144 q^{92} + 36 q^{93} + 162 q^{94} + 162 q^{95} + 288 q^{96} + 162 q^{97} + 378 q^{98} + 108 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(333))\)

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
333.2.a \(\chi_{333}(1, \cdot)\) 333.2.a.a 1 1
333.2.a.b 1
333.2.a.c 1
333.2.a.d 1
333.2.a.e 3
333.2.a.f 4
333.2.a.g 4
333.2.c \(\chi_{333}(73, \cdot)\) 333.2.c.a 2 1
333.2.c.b 2
333.2.c.c 4
333.2.c.d 8
333.2.e \(\chi_{333}(112, \cdot)\) 333.2.e.a 36 2
333.2.e.b 36
333.2.f \(\chi_{333}(10, \cdot)\) 333.2.f.a 2 2
333.2.f.b 6
333.2.f.c 10
333.2.f.d 12
333.2.g \(\chi_{333}(211, \cdot)\) 333.2.g.a 72 2
333.2.h \(\chi_{333}(121, \cdot)\) 333.2.h.a 72 2
333.2.j \(\chi_{333}(80, \cdot)\) 333.2.j.a 28 2
333.2.k \(\chi_{333}(175, \cdot)\) 333.2.k.a 2 2
333.2.k.b 4
333.2.k.c 66
333.2.q \(\chi_{333}(184, \cdot)\) 333.2.q.a 8 2
333.2.q.b 12
333.2.q.c 52
333.2.s \(\chi_{333}(64, \cdot)\) 333.2.s.a 2 2
333.2.s.b 4
333.2.s.c 4
333.2.s.d 6
333.2.s.e 8
333.2.s.f 8
333.2.t \(\chi_{333}(85, \cdot)\) 333.2.t.a 2 2
333.2.t.b 4
333.2.t.c 66
333.2.w \(\chi_{333}(7, \cdot)\) 333.2.w.a 216 6
333.2.x \(\chi_{333}(46, \cdot)\) 333.2.x.a 6 6
333.2.x.b 6
333.2.x.c 6
333.2.x.d 18
333.2.x.e 24
333.2.x.f 24
333.2.y \(\chi_{333}(16, \cdot)\) 333.2.y.a 216 6
333.2.z \(\chi_{333}(14, \cdot)\) 333.2.z.a 144 4
333.2.bc \(\chi_{333}(68, \cdot)\) 333.2.bc.a 144 4
333.2.be \(\chi_{333}(8, \cdot)\) 333.2.be.a 56 4
333.2.bf \(\chi_{333}(140, \cdot)\) 333.2.bf.a 144 4
333.2.bl \(\chi_{333}(28, \cdot)\) 333.2.bl.a 6 6
333.2.bl.b 12
333.2.bl.c 18
333.2.bl.d 18
333.2.bl.e 36
333.2.bm \(\chi_{333}(58, \cdot)\) 333.2.bm.a 216 6
333.2.bp \(\chi_{333}(4, \cdot)\) 333.2.bp.a 216 6
333.2.br \(\chi_{333}(17, \cdot)\) 333.2.br.a 144 12
333.2.bs \(\chi_{333}(56, \cdot)\) 333.2.bs.a 432 12
333.2.bv \(\chi_{333}(2, \cdot)\) 333.2.bv.a 432 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(333))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(333)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 2}\)