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Properties

Label 2050.2
Level 2050
Weight 2
Dimension 38662
Nonzero newspaces 56
Sturm bound 504000
Trace bound 22

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Defining parameters

Level: \( N \) = \( 2050 = 2 \cdot 5^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(504000\)
Trace bound: \(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2050))\).

Total New Old
Modular forms 128240 38662 89578
Cusp forms 123761 38662 85099
Eisenstein series 4479 0 4479

Trace form

\( 38662 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} + 26 q^{9} + O(q^{10}) \) \( 38662 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} + 26 q^{9} + 10 q^{10} + 24 q^{11} + 8 q^{12} + 28 q^{13} + 16 q^{14} + 40 q^{15} + 2 q^{16} - 4 q^{17} - 24 q^{18} - 40 q^{19} - 16 q^{21} - 56 q^{22} - 32 q^{23} - 32 q^{24} - 70 q^{25} - 12 q^{26} - 40 q^{27} - 24 q^{28} - 20 q^{29} - 40 q^{30} + 24 q^{31} + 2 q^{32} + 136 q^{33} + 36 q^{34} + 40 q^{35} + 46 q^{36} + 186 q^{37} + 80 q^{38} + 192 q^{39} + 10 q^{40} + 62 q^{41} + 224 q^{42} + 48 q^{43} + 64 q^{44} - 30 q^{45} + 88 q^{46} + 136 q^{47} + 28 q^{48} + 104 q^{49} + 50 q^{50} + 144 q^{51} + 38 q^{52} + 58 q^{53} + 120 q^{54} + 40 q^{55} + 16 q^{56} + 60 q^{58} + 4 q^{61} - 56 q^{62} - 72 q^{63} + 2 q^{64} - 70 q^{65} - 24 q^{66} + 36 q^{67} - 84 q^{68} - 8 q^{69} - 80 q^{70} + 64 q^{71} + 26 q^{72} + 68 q^{73} - 124 q^{74} - 120 q^{75} - 40 q^{76} - 48 q^{77} - 88 q^{78} + 80 q^{79} + 10 q^{80} + 252 q^{81} - 38 q^{82} - 72 q^{83} - 56 q^{84} - 30 q^{85} - 32 q^{86} + 40 q^{87} + 24 q^{88} + 50 q^{89} + 10 q^{90} + 224 q^{91} + 8 q^{92} + 216 q^{93} + 96 q^{94} + 120 q^{95} + 8 q^{96} + 236 q^{97} + 114 q^{98} + 252 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2050))\)

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
2050.2.a \(\chi_{2050}(1, \cdot)\) 2050.2.a.a 1 1
2050.2.a.b 1
2050.2.a.c 1
2050.2.a.d 1
2050.2.a.e 1
2050.2.a.f 1
2050.2.a.g 1
2050.2.a.h 2
2050.2.a.i 2
2050.2.a.j 2
2050.2.a.k 2
2050.2.a.l 2
2050.2.a.m 2
2050.2.a.n 2
2050.2.a.o 2
2050.2.a.p 2
2050.2.a.q 3
2050.2.a.r 3
2050.2.a.s 3
2050.2.a.t 3
2050.2.a.u 3
2050.2.a.v 4
2050.2.a.w 4
2050.2.a.x 7
2050.2.a.y 7
2050.2.b \(\chi_{2050}(901, \cdot)\) 2050.2.b.a 2 1
2050.2.b.b 2
2050.2.b.c 2
2050.2.b.d 2
2050.2.b.e 2
2050.2.b.f 2
2050.2.b.g 2
2050.2.b.h 4
2050.2.b.i 4
2050.2.b.j 4
2050.2.b.k 4
2050.2.b.l 8
2050.2.b.m 8
2050.2.b.n 10
2050.2.b.o 10
2050.2.c \(\chi_{2050}(1149, \cdot)\) 2050.2.c.a 2 1
2050.2.c.b 2
2050.2.c.c 2
2050.2.c.d 2
2050.2.c.e 2
2050.2.c.f 2
2050.2.c.g 4
2050.2.c.h 4
2050.2.c.i 4
2050.2.c.j 4
2050.2.c.k 4
2050.2.c.l 4
2050.2.c.m 4
2050.2.c.n 6
2050.2.c.o 6
2050.2.c.p 8
2050.2.d \(\chi_{2050}(2049, \cdot)\) 2050.2.d.a 2 1
2050.2.d.b 2
2050.2.d.c 2
2050.2.d.d 2
2050.2.d.e 2
2050.2.d.f 2
2050.2.d.g 4
2050.2.d.h 4
2050.2.d.i 4
2050.2.d.j 4
2050.2.d.k 4
2050.2.d.l 8
2050.2.d.m 8
2050.2.d.n 16
2050.2.g \(\chi_{2050}(1549, \cdot)\) n/a 124 2
2050.2.h \(\chi_{2050}(401, \cdot)\) n/a 134 2
2050.2.k \(\chi_{2050}(141, \cdot)\) n/a 424 4
2050.2.l \(\chi_{2050}(461, \cdot)\) n/a 424 4
2050.2.m \(\chi_{2050}(221, \cdot)\) n/a 424 4
2050.2.n \(\chi_{2050}(961, \cdot)\) n/a 424 4
2050.2.o \(\chi_{2050}(411, \cdot)\) n/a 400 4
2050.2.p \(\chi_{2050}(51, \cdot)\) n/a 264 4
2050.2.r \(\chi_{2050}(407, \cdot)\) n/a 252 4
2050.2.s \(\chi_{2050}(243, \cdot)\) n/a 252 4
2050.2.u \(\chi_{2050}(549, \cdot)\) n/a 256 4
2050.2.v \(\chi_{2050}(351, \cdot)\) n/a 264 4
2050.2.w \(\chi_{2050}(769, \cdot)\) n/a 416 4
2050.2.x \(\chi_{2050}(189, \cdot)\) n/a 416 4
2050.2.y \(\chi_{2050}(209, \cdot)\) n/a 416 4
2050.2.z \(\chi_{2050}(269, \cdot)\) n/a 416 4
2050.2.ba \(\chi_{2050}(409, \cdot)\) n/a 416 4
2050.2.bb \(\chi_{2050}(329, \cdot)\) n/a 400 4
2050.2.bc \(\chi_{2050}(81, \cdot)\) n/a 424 4
2050.2.bd \(\chi_{2050}(31, \cdot)\) n/a 424 4
2050.2.be \(\chi_{2050}(469, \cdot)\) n/a 416 4
2050.2.bf \(\chi_{2050}(789, \cdot)\) n/a 416 4
2050.2.bg \(\chi_{2050}(59, \cdot)\) n/a 416 4
2050.2.bh \(\chi_{2050}(271, \cdot)\) n/a 424 4
2050.2.bi \(\chi_{2050}(291, \cdot)\) n/a 424 4
2050.2.bj \(\chi_{2050}(1671, \cdot)\) n/a 424 4
2050.2.bk \(\chi_{2050}(529, \cdot)\) n/a 416 4
2050.2.bl \(\chi_{2050}(599, \cdot)\) n/a 256 4
2050.2.bt \(\chi_{2050}(251, \cdot)\) n/a 536 8
2050.2.bu \(\chi_{2050}(49, \cdot)\) n/a 496 8
2050.2.cb \(\chi_{2050}(61, \cdot)\) n/a 832 8
2050.2.cc \(\chi_{2050}(169, \cdot)\) n/a 848 8
2050.2.cd \(\chi_{2050}(159, \cdot)\) n/a 848 8
2050.2.ce \(\chi_{2050}(91, \cdot)\) n/a 832 8
2050.2.cf \(\chi_{2050}(21, \cdot)\) n/a 832 8
2050.2.cg \(\chi_{2050}(131, \cdot)\) n/a 832 8
2050.2.ch \(\chi_{2050}(39, \cdot)\) n/a 848 8
2050.2.ci \(\chi_{2050}(459, \cdot)\) n/a 848 8
2050.2.cj \(\chi_{2050}(9, \cdot)\) n/a 848 8
2050.2.ck \(\chi_{2050}(121, \cdot)\) n/a 832 8
2050.2.dc \(\chi_{2050}(183, \cdot)\) n/a 1680 16
2050.2.dd \(\chi_{2050}(47, \cdot)\) n/a 1680 16
2050.2.de \(\chi_{2050}(117, \cdot)\) n/a 1680 16
2050.2.df \(\chi_{2050}(13, \cdot)\) n/a 1680 16
2050.2.dg \(\chi_{2050}(17, \cdot)\) n/a 1680 16
2050.2.dh \(\chi_{2050}(93, \cdot)\) n/a 1008 16
2050.2.di \(\chi_{2050}(3, \cdot)\) n/a 1680 16
2050.2.dj \(\chi_{2050}(167, \cdot)\) n/a 1680 16
2050.2.dk \(\chi_{2050}(263, \cdot)\) n/a 1680 16
2050.2.dl \(\chi_{2050}(7, \cdot)\) n/a 1008 16
2050.2.dm \(\chi_{2050}(63, \cdot)\) n/a 1680 16
2050.2.dn \(\chi_{2050}(217, \cdot)\) n/a 1680 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2050))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2050)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(205))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(410))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1025))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2050))\)\(^{\oplus 1}\)