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Properties

Label 801.2
Level 801
Weight 2
Dimension 18414
Nonzero newspaces 16
Newform subspaces 42
Sturm bound 95040
Trace bound 5

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Defining parameters

Level: \( N \) = \( 801 = 3^{2} \cdot 89 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 42 \)
Sturm bound: \(95040\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(801))\).

Total New Old
Modular forms 24464 19196 5268
Cusp forms 23057 18414 4643
Eisenstein series 1407 782 625

Trace form

\( 18414 q - 132 q^{2} - 176 q^{3} - 132 q^{4} - 132 q^{5} - 176 q^{6} - 132 q^{7} - 132 q^{8} - 176 q^{9} + O(q^{10}) \) \( 18414 q - 132 q^{2} - 176 q^{3} - 132 q^{4} - 132 q^{5} - 176 q^{6} - 132 q^{7} - 132 q^{8} - 176 q^{9} - 396 q^{10} - 132 q^{11} - 176 q^{12} - 132 q^{13} - 132 q^{14} - 176 q^{15} - 132 q^{16} - 132 q^{17} - 176 q^{18} - 396 q^{19} - 132 q^{20} - 176 q^{21} - 132 q^{22} - 132 q^{23} - 176 q^{24} - 132 q^{25} - 132 q^{26} - 176 q^{27} - 396 q^{28} - 132 q^{29} - 176 q^{30} - 132 q^{31} - 132 q^{32} - 176 q^{33} - 132 q^{34} - 132 q^{35} - 176 q^{36} - 396 q^{37} - 132 q^{38} - 176 q^{39} - 132 q^{40} - 132 q^{41} - 176 q^{42} - 132 q^{43} - 132 q^{44} - 176 q^{45} - 396 q^{46} - 132 q^{47} - 176 q^{48} - 132 q^{49} - 132 q^{50} - 176 q^{51} - 132 q^{52} - 132 q^{53} - 176 q^{54} - 396 q^{55} - 132 q^{56} - 176 q^{57} - 132 q^{58} - 132 q^{59} - 176 q^{60} - 132 q^{61} - 132 q^{62} - 176 q^{63} - 396 q^{64} - 132 q^{65} - 176 q^{66} - 132 q^{67} - 132 q^{68} - 176 q^{69} - 132 q^{70} - 132 q^{71} - 176 q^{72} - 440 q^{73} - 242 q^{74} - 176 q^{75} - 396 q^{76} - 220 q^{77} - 176 q^{78} - 220 q^{79} - 462 q^{80} - 176 q^{81} - 572 q^{82} - 264 q^{83} - 176 q^{84} - 264 q^{85} - 308 q^{86} - 176 q^{87} - 440 q^{88} - 308 q^{89} - 352 q^{90} - 572 q^{91} - 396 q^{92} - 176 q^{93} - 308 q^{94} - 264 q^{95} - 176 q^{96} - 264 q^{97} - 308 q^{98} - 176 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(801))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
801.2.a \(\chi_{801}(1, \cdot)\) 801.2.a.a 1 1
801.2.a.b 1
801.2.a.c 1
801.2.a.d 1
801.2.a.e 3
801.2.a.f 3
801.2.a.g 3
801.2.a.h 4
801.2.a.i 5
801.2.a.j 7
801.2.a.k 7
801.2.d \(\chi_{801}(622, \cdot)\) 801.2.d.a 2 1
801.2.d.b 6
801.2.d.c 6
801.2.d.d 6
801.2.d.e 16
801.2.e \(\chi_{801}(268, \cdot)\) 801.2.e.a 76 2
801.2.e.b 100
801.2.g \(\chi_{801}(55, \cdot)\) 801.2.g.a 14 2
801.2.g.b 28
801.2.g.c 32
801.2.h \(\chi_{801}(88, \cdot)\) 801.2.h.a 176 2
801.2.k \(\chi_{801}(215, \cdot)\) 801.2.k.a 60 4
801.2.k.b 60
801.2.m \(\chi_{801}(64, \cdot)\) 801.2.m.a 60 10
801.2.m.b 80
801.2.m.c 80
801.2.m.d 140
801.2.n \(\chi_{801}(34, \cdot)\) 801.2.n.a 352 4
801.2.p \(\chi_{801}(73, \cdot)\) 801.2.p.a 60 10
801.2.p.b 140
801.2.p.c 160
801.2.t \(\chi_{801}(77, \cdot)\) 801.2.t.a 704 8
801.2.u \(\chi_{801}(4, \cdot)\) 801.2.u.a 1760 20
801.2.v \(\chi_{801}(10, \cdot)\) 801.2.v.a 140 20
801.2.v.b 280
801.2.v.c 320
801.2.z \(\chi_{801}(22, \cdot)\) 801.2.z.a 1760 20
801.2.bb \(\chi_{801}(26, \cdot)\) 801.2.bb.a 600 40
801.2.bb.b 600
801.2.bd \(\chi_{801}(40, \cdot)\) 801.2.bd.a 3520 40
801.2.be \(\chi_{801}(14, \cdot)\) 801.2.be.a 7040 80

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(801))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(801)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(89))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(267))\)\(^{\oplus 2}\)