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Properties

Label 2064.2
Level 2064
Weight 2
Dimension 49472
Nonzero newspaces 32
Sturm bound 473088
Trace bound 12

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Defining parameters

Level: \( N \) = \( 2064 = 2^{4} \cdot 3 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(473088\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2064))\).

Total New Old
Modular forms 120624 50212 70412
Cusp forms 115921 49472 66449
Eisenstein series 4703 740 3963

Trace form

\( 49472 q - 61 q^{3} - 152 q^{4} + 4 q^{5} - 68 q^{6} - 110 q^{7} + 24 q^{8} - 11 q^{9} + O(q^{10}) \) \( 49472 q - 61 q^{3} - 152 q^{4} + 4 q^{5} - 68 q^{6} - 110 q^{7} + 24 q^{8} - 11 q^{9} - 152 q^{10} + 24 q^{11} - 84 q^{12} - 190 q^{13} - 24 q^{14} - 43 q^{15} - 200 q^{16} - 4 q^{17} - 100 q^{18} - 94 q^{19} - 32 q^{20} - 113 q^{21} - 200 q^{22} - 16 q^{23} - 140 q^{24} - 60 q^{25} - 40 q^{26} - 85 q^{27} - 168 q^{28} + 20 q^{29} - 124 q^{30} - 158 q^{31} - 173 q^{33} - 152 q^{34} - 48 q^{35} - 116 q^{36} - 142 q^{37} + 16 q^{38} - 99 q^{39} - 120 q^{40} + 12 q^{41} + 4 q^{42} - 126 q^{43} + 80 q^{44} - 77 q^{45} - 72 q^{46} + 44 q^{48} - 288 q^{49} + 72 q^{50} - 131 q^{51} - 104 q^{52} - 28 q^{53} + 12 q^{54} - 190 q^{55} - 5 q^{57} - 200 q^{58} - 56 q^{59} - 100 q^{60} - 318 q^{61} + 24 q^{62} - 79 q^{63} - 296 q^{64} + 24 q^{65} - 188 q^{66} - 158 q^{67} - 64 q^{68} - 161 q^{69} - 312 q^{70} + 16 q^{71} - 156 q^{72} - 102 q^{73} - 104 q^{74} - 25 q^{75} - 296 q^{76} - 32 q^{77} - 180 q^{78} - 94 q^{79} - 16 q^{80} - 203 q^{81} - 216 q^{82} + 72 q^{83} - 68 q^{84} - 192 q^{85} + 16 q^{86} - 18 q^{87} - 104 q^{88} + 12 q^{89} - 36 q^{90} + 2 q^{91} + 32 q^{92} - 73 q^{93} - 88 q^{94} + 112 q^{95} + 28 q^{96} - 310 q^{97} + 80 q^{98} + 65 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2064))\)

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
2064.2.a \(\chi_{2064}(1, \cdot)\) 2064.2.a.a 1 1
2064.2.a.b 1
2064.2.a.c 1
2064.2.a.d 1
2064.2.a.e 1
2064.2.a.f 1
2064.2.a.g 1
2064.2.a.h 1
2064.2.a.i 1
2064.2.a.j 1
2064.2.a.k 1
2064.2.a.l 1
2064.2.a.m 1
2064.2.a.n 1
2064.2.a.o 1
2064.2.a.p 1
2064.2.a.q 2
2064.2.a.r 2
2064.2.a.s 2
2064.2.a.t 2
2064.2.a.u 2
2064.2.a.v 2
2064.2.a.w 2
2064.2.a.x 3
2064.2.a.y 3
2064.2.a.z 3
2064.2.a.ba 3
2064.2.b \(\chi_{2064}(1289, \cdot)\) None 0 1
2064.2.d \(\chi_{2064}(431, \cdot)\) 2064.2.d.a 8 1
2064.2.d.b 28
2064.2.d.c 48
2064.2.g \(\chi_{2064}(1033, \cdot)\) None 0 1
2064.2.i \(\chi_{2064}(1375, \cdot)\) 2064.2.i.a 8 1
2064.2.i.b 8
2064.2.i.c 14
2064.2.i.d 14
2064.2.j \(\chi_{2064}(1463, \cdot)\) None 0 1
2064.2.l \(\chi_{2064}(257, \cdot)\) 2064.2.l.a 2 1
2064.2.l.b 2
2064.2.l.c 2
2064.2.l.d 2
2064.2.l.e 2
2064.2.l.f 6
2064.2.l.g 6
2064.2.l.h 12
2064.2.l.i 12
2064.2.l.j 20
2064.2.l.k 20
2064.2.o \(\chi_{2064}(343, \cdot)\) None 0 1
2064.2.q \(\chi_{2064}(49, \cdot)\) 2064.2.q.a 2 2
2064.2.q.b 2
2064.2.q.c 2
2064.2.q.d 2
2064.2.q.e 2
2064.2.q.f 2
2064.2.q.g 2
2064.2.q.h 2
2064.2.q.i 4
2064.2.q.j 6
2064.2.q.k 6
2064.2.q.l 6
2064.2.q.m 6
2064.2.q.n 6
2064.2.q.o 8
2064.2.q.p 8
2064.2.q.q 10
2064.2.q.r 12
2064.2.t \(\chi_{2064}(517, \cdot)\) n/a 336 2
2064.2.u \(\chi_{2064}(859, \cdot)\) n/a 352 2
2064.2.v \(\chi_{2064}(947, \cdot)\) n/a 672 2
2064.2.w \(\chi_{2064}(773, \cdot)\) n/a 696 2
2064.2.ba \(\chi_{2064}(7, \cdot)\) None 0 2
2064.2.bd \(\chi_{2064}(209, \cdot)\) n/a 172 2
2064.2.bf \(\chi_{2064}(1511, \cdot)\) None 0 2
2064.2.bg \(\chi_{2064}(1039, \cdot)\) 2064.2.bg.a 2 2
2064.2.bg.b 2
2064.2.bg.c 2
2064.2.bg.d 2
2064.2.bg.e 2
2064.2.bg.f 2
2064.2.bg.g 10
2064.2.bg.h 10
2064.2.bg.i 14
2064.2.bg.j 14
2064.2.bg.k 14
2064.2.bg.l 14
2064.2.bi \(\chi_{2064}(1081, \cdot)\) None 0 2
2064.2.bl \(\chi_{2064}(479, \cdot)\) n/a 176 2
2064.2.bn \(\chi_{2064}(953, \cdot)\) None 0 2
2064.2.bo \(\chi_{2064}(97, \cdot)\) n/a 264 6
2064.2.br \(\chi_{2064}(437, \cdot)\) n/a 1392 4
2064.2.bs \(\chi_{2064}(251, \cdot)\) n/a 1392 4
2064.2.bt \(\chi_{2064}(523, \cdot)\) n/a 704 4
2064.2.bu \(\chi_{2064}(565, \cdot)\) n/a 704 4
2064.2.by \(\chi_{2064}(65, \cdot)\) n/a 516 6
2064.2.ca \(\chi_{2064}(551, \cdot)\) None 0 6
2064.2.cc \(\chi_{2064}(151, \cdot)\) None 0 6
2064.2.cf \(\chi_{2064}(47, \cdot)\) n/a 528 6
2064.2.ch \(\chi_{2064}(137, \cdot)\) None 0 6
2064.2.ci \(\chi_{2064}(223, \cdot)\) n/a 264 6
2064.2.ck \(\chi_{2064}(121, \cdot)\) None 0 6
2064.2.cm \(\chi_{2064}(289, \cdot)\) n/a 528 12
2064.2.cn \(\chi_{2064}(211, \cdot)\) n/a 2112 12
2064.2.co \(\chi_{2064}(133, \cdot)\) n/a 2112 12
2064.2.ct \(\chi_{2064}(125, \cdot)\) n/a 4176 12
2064.2.cu \(\chi_{2064}(11, \cdot)\) n/a 4176 12
2064.2.cw \(\chi_{2064}(25, \cdot)\) None 0 12
2064.2.cy \(\chi_{2064}(175, \cdot)\) n/a 528 12
2064.2.cz \(\chi_{2064}(89, \cdot)\) None 0 12
2064.2.db \(\chi_{2064}(95, \cdot)\) n/a 1056 12
2064.2.de \(\chi_{2064}(55, \cdot)\) None 0 12
2064.2.dg \(\chi_{2064}(23, \cdot)\) None 0 12
2064.2.di \(\chi_{2064}(449, \cdot)\) n/a 1032 12
2064.2.dk \(\chi_{2064}(83, \cdot)\) n/a 8352 24
2064.2.dl \(\chi_{2064}(5, \cdot)\) n/a 8352 24
2064.2.dq \(\chi_{2064}(13, \cdot)\) n/a 4224 24
2064.2.dr \(\chi_{2064}(19, \cdot)\) n/a 4224 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2064))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2064)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(172))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(258))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(344))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(516))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(688))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1032))\)\(^{\oplus 2}\)