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Properties

Label 333.3
Level 333
Weight 3
Dimension 6332
Nonzero newspaces 24
Newform subspaces 34
Sturm bound 24624
Trace bound 9

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Defining parameters

Level: \( N \) = \( 333 = 3^{2} \cdot 37 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 34 \)
Sturm bound: \(24624\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(333))\).

Total New Old
Modular forms 8496 6648 1848
Cusp forms 7920 6332 1588
Eisenstein series 576 316 260

Trace form

\( 6332 q - 48 q^{2} - 66 q^{3} - 52 q^{4} - 66 q^{5} - 90 q^{6} - 50 q^{7} - 54 q^{8} - 54 q^{9} + O(q^{10}) \) \( 6332 q - 48 q^{2} - 66 q^{3} - 52 q^{4} - 66 q^{5} - 90 q^{6} - 50 q^{7} - 54 q^{8} - 54 q^{9} - 138 q^{10} - 48 q^{11} - 84 q^{12} - 62 q^{13} - 66 q^{14} - 72 q^{15} - 76 q^{16} - 54 q^{17} - 72 q^{18} - 206 q^{19} - 42 q^{20} - 60 q^{21} - 60 q^{22} + 42 q^{23} + 18 q^{24} - 28 q^{25} + 36 q^{26} - 180 q^{27} + 310 q^{28} - 84 q^{29} - 108 q^{30} + 280 q^{31} + 180 q^{32} - 90 q^{33} + 144 q^{34} - 54 q^{36} - 136 q^{37} - 114 q^{38} - 24 q^{39} - 654 q^{40} - 282 q^{41} - 72 q^{42} - 428 q^{43} - 630 q^{44} + 36 q^{45} - 1074 q^{46} - 84 q^{47} - 138 q^{48} - 456 q^{49} - 258 q^{50} - 234 q^{51} - 62 q^{52} - 54 q^{53} + 90 q^{54} - 138 q^{55} + 6 q^{56} - 6 q^{57} + 372 q^{58} + 276 q^{59} - 108 q^{60} + 598 q^{61} + 936 q^{62} - 144 q^{63} + 1256 q^{64} + 546 q^{65} - 36 q^{66} + 100 q^{67} + 540 q^{68} - 72 q^{69} + 516 q^{70} + 90 q^{71} - 486 q^{72} - 404 q^{73} - 300 q^{74} - 66 q^{75} - 536 q^{76} - 354 q^{77} - 144 q^{78} - 410 q^{79} - 1440 q^{80} + 90 q^{81} - 1218 q^{82} - 246 q^{83} - 60 q^{84} - 918 q^{85} - 1326 q^{86} + 396 q^{87} - 1434 q^{88} - 774 q^{89} - 180 q^{90} - 1120 q^{91} - 4380 q^{92} - 2292 q^{93} - 3678 q^{94} - 3426 q^{95} - 5112 q^{96} - 3092 q^{97} - 5238 q^{98} - 2052 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(333))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
333.3.b \(\chi_{333}(260, \cdot)\) 333.3.b.a 24 1
333.3.d \(\chi_{333}(332, \cdot)\) 333.3.d.a 24 1
333.3.i \(\chi_{333}(154, \cdot)\) 333.3.i.a 12 2
333.3.i.b 24
333.3.i.c 24
333.3.l \(\chi_{333}(137, \cdot)\) 333.3.l.a 148 2
333.3.m \(\chi_{333}(233, \cdot)\) 333.3.m.a 8 2
333.3.m.b 40
333.3.n \(\chi_{333}(110, \cdot)\) 333.3.n.a 148 2
333.3.o \(\chi_{333}(101, \cdot)\) 333.3.o.a 148 2
333.3.p \(\chi_{333}(26, \cdot)\) 333.3.p.a 48 2
333.3.r \(\chi_{333}(38, \cdot)\) 333.3.r.a 144 2
333.3.u \(\chi_{333}(47, \cdot)\) 333.3.u.a 148 2
333.3.v \(\chi_{333}(11, \cdot)\) 333.3.v.a 148 2
333.3.ba \(\chi_{333}(214, \cdot)\) 333.3.ba.a 296 4
333.3.bb \(\chi_{333}(82, \cdot)\) 333.3.bb.a 24 4
333.3.bb.b 24
333.3.bb.c 24
333.3.bb.d 48
333.3.bd \(\chi_{333}(31, \cdot)\) 333.3.bd.a 296 4
333.3.bg \(\chi_{333}(88, \cdot)\) 333.3.bg.a 296 4
333.3.bh \(\chi_{333}(41, \cdot)\) 333.3.bh.a 444 6
333.3.bi \(\chi_{333}(62, \cdot)\) 333.3.bi.a 156 6
333.3.bj \(\chi_{333}(95, \cdot)\) 333.3.bj.a 444 6
333.3.bk \(\chi_{333}(83, \cdot)\) 333.3.bk.a 444 6
333.3.bn \(\chi_{333}(86, \cdot)\) 333.3.bn.a 444 6
333.3.bo \(\chi_{333}(44, \cdot)\) 333.3.bo.a 156 6
333.3.bq \(\chi_{333}(13, \cdot)\) 333.3.bq.a 888 12
333.3.bt \(\chi_{333}(22, \cdot)\) 333.3.bt.a 888 12
333.3.bu \(\chi_{333}(19, \cdot)\) 333.3.bu.a 12 12
333.3.bu.b 60
333.3.bu.c 72
333.3.bu.d 84
333.3.bu.e 144

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(333))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(333)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(333))\)\(^{\oplus 1}\)