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Properties

Label 494.2
Level 494
Weight 2
Dimension 2479
Nonzero newspaces 24
Newform subspaces 60
Sturm bound 30240
Trace bound 13

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Defining parameters

Level: \( N \) = \( 494 = 2 \cdot 13 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 60 \)
Sturm bound: \(30240\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(494))\).

Total New Old
Modular forms 7992 2479 5513
Cusp forms 7129 2479 4650
Eisenstein series 863 0 863

Trace form

\( 2479 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 12 q^{6} + 16 q^{7} - 3 q^{8} + 7 q^{9} + O(q^{10}) \) \( 2479 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 12 q^{6} + 16 q^{7} - 3 q^{8} + 7 q^{9} - 12 q^{10} + 12 q^{11} - 8 q^{12} - 45 q^{13} - 36 q^{14} - 48 q^{15} - 5 q^{16} - 12 q^{17} - 45 q^{18} - 73 q^{19} - 24 q^{20} - 44 q^{21} - 18 q^{22} + 12 q^{23} + 12 q^{24} - 9 q^{25} + 9 q^{26} - 18 q^{27} + 4 q^{28} - 24 q^{29} + 24 q^{30} - 20 q^{31} + 3 q^{32} - 84 q^{33} + 6 q^{34} - 72 q^{35} - 9 q^{36} + 16 q^{37} + 3 q^{38} - 50 q^{39} + 18 q^{40} - 12 q^{41} + 24 q^{42} - 40 q^{43} - 30 q^{44} - 132 q^{45} - 48 q^{46} - 96 q^{47} - 6 q^{48} - 13 q^{49} - 105 q^{50} - 126 q^{51} + 7 q^{52} - 54 q^{53} - 60 q^{54} - 48 q^{55} - 72 q^{56} - 88 q^{57} - 36 q^{58} - 96 q^{59} - 48 q^{60} - 48 q^{61} - 84 q^{62} - 128 q^{63} - 15 q^{64} - 120 q^{65} - 96 q^{66} - 104 q^{67} + 30 q^{68} - 60 q^{69} - 72 q^{71} - 27 q^{72} - 20 q^{73} + 36 q^{74} - 8 q^{75} + 11 q^{76} - 24 q^{77} - 48 q^{78} - 108 q^{79} + 12 q^{80} - 83 q^{81} - 48 q^{82} - 84 q^{83} - 68 q^{84} - 66 q^{85} + 12 q^{86} - 240 q^{87} + 36 q^{88} - 66 q^{89} - 66 q^{90} - 32 q^{91} - 48 q^{92} - 140 q^{93} - 120 q^{94} - 18 q^{95} + 12 q^{96} - 86 q^{97} - 69 q^{98} - 162 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(494))\)

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
494.2.a \(\chi_{494}(1, \cdot)\) 494.2.a.a 1 1
494.2.a.b 1
494.2.a.c 1
494.2.a.d 1
494.2.a.e 3
494.2.a.f 3
494.2.a.g 3
494.2.a.h 4
494.2.d \(\chi_{494}(77, \cdot)\) 494.2.d.a 2 1
494.2.d.b 6
494.2.d.c 14
494.2.e \(\chi_{494}(87, \cdot)\) 494.2.e.a 2 2
494.2.e.b 2
494.2.e.c 18
494.2.e.d 22
494.2.f \(\chi_{494}(235, \cdot)\) 494.2.f.a 2 2
494.2.f.b 2
494.2.f.c 2
494.2.f.d 2
494.2.f.e 4
494.2.f.f 4
494.2.f.g 4
494.2.f.h 6
494.2.f.i 6
494.2.f.j 8
494.2.g \(\chi_{494}(191, \cdot)\) 494.2.g.a 2 2
494.2.g.b 6
494.2.g.c 6
494.2.g.d 6
494.2.g.e 8
494.2.g.f 12
494.2.h \(\chi_{494}(315, \cdot)\) 494.2.h.a 2 2
494.2.h.b 2
494.2.h.c 18
494.2.h.d 22
494.2.i \(\chi_{494}(151, \cdot)\) 494.2.i.a 52 2
494.2.m \(\chi_{494}(153, \cdot)\) 494.2.m.a 16 2
494.2.m.b 28
494.2.n \(\chi_{494}(311, \cdot)\) 494.2.n.a 52 2
494.2.o \(\chi_{494}(277, \cdot)\) 494.2.o.a 44 2
494.2.v \(\chi_{494}(49, \cdot)\) 494.2.v.a 44 2
494.2.w \(\chi_{494}(35, \cdot)\) 494.2.w.a 72 6
494.2.w.b 72
494.2.x \(\chi_{494}(131, \cdot)\) 494.2.x.a 6 6
494.2.x.b 18
494.2.x.c 30
494.2.x.d 30
494.2.x.e 36
494.2.y \(\chi_{494}(9, \cdot)\) 494.2.y.a 72 6
494.2.y.b 72
494.2.z \(\chi_{494}(141, \cdot)\) 494.2.z.a 88 4
494.2.bd \(\chi_{494}(145, \cdot)\) 494.2.bd.a 88 4
494.2.be \(\chi_{494}(37, \cdot)\) 494.2.be.a 88 4
494.2.bf \(\chi_{494}(31, \cdot)\) 494.2.bf.a 104 4
494.2.bh \(\chi_{494}(199, \cdot)\) 494.2.bh.a 144 6
494.2.bl \(\chi_{494}(25, \cdot)\) 494.2.bl.a 132 6
494.2.bm \(\chi_{494}(17, \cdot)\) 494.2.bm.a 144 6
494.2.bt \(\chi_{494}(41, \cdot)\) 494.2.bt.a 288 12
494.2.bu \(\chi_{494}(15, \cdot)\) 494.2.bu.a 288 12
494.2.bv \(\chi_{494}(21, \cdot)\) 494.2.bv.a 264 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(494))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(494)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(247))\)\(^{\oplus 2}\)