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Properties

Label 2006.2
Level 2006
Weight 2
Dimension 41449
Nonzero newspaces 10
Sturm bound 501120
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2006 = 2 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(501120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2006))\).

Total New Old
Modular forms 127136 41449 85687
Cusp forms 123425 41449 81976
Eisenstein series 3711 0 3711

Trace form

\( 41449 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 12 q^{6} + 24 q^{7} + 3 q^{8} + 39 q^{9} + O(q^{10}) \) \( 41449 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 12 q^{6} + 24 q^{7} + 3 q^{8} + 39 q^{9} + 10 q^{10} + 4 q^{11} - 4 q^{12} + 10 q^{13} - 8 q^{14} - 24 q^{15} - 5 q^{16} + 3 q^{17} - 25 q^{18} + 28 q^{19} + 10 q^{20} + 4 q^{22} + 40 q^{23} - 4 q^{24} + 21 q^{25} + 34 q^{26} + 72 q^{27} + 24 q^{28} + 50 q^{29} + 72 q^{30} + 32 q^{31} + 3 q^{32} + 80 q^{33} + 35 q^{34} + 80 q^{35} + 39 q^{36} + 50 q^{37} + 44 q^{38} + 40 q^{39} + 18 q^{40} - 10 q^{41} + 20 q^{43} - 28 q^{44} - 50 q^{45} - 108 q^{46} - 132 q^{47} + 12 q^{48} - 189 q^{49} - 251 q^{50} - 220 q^{51} - 138 q^{52} - 206 q^{53} - 398 q^{54} - 292 q^{55} + 24 q^{56} - 516 q^{57} - 90 q^{58} - 193 q^{59} - 340 q^{60} - 142 q^{61} - 116 q^{62} - 460 q^{63} + 3 q^{64} - 168 q^{65} - 278 q^{66} - 60 q^{67} - 31 q^{68} - 304 q^{69} - 152 q^{70} - 112 q^{71} - q^{72} - 62 q^{73} - 74 q^{74} + 32 q^{75} + 60 q^{76} + 128 q^{77} + 40 q^{78} + 80 q^{79} - 14 q^{80} + 155 q^{81} - 10 q^{82} + 108 q^{83} + 32 q^{84} - 54 q^{85} + 68 q^{86} + 72 q^{87} - 28 q^{88} + 78 q^{89} + 98 q^{90} + 16 q^{91} + 40 q^{92} + 128 q^{93} + 16 q^{94} + 72 q^{95} + 12 q^{96} + 102 q^{97} + 99 q^{98} - 74 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2006))\)

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
2006.2.a \(\chi_{2006}(1, \cdot)\) 2006.2.a.a 1 1
2006.2.a.b 1
2006.2.a.c 1
2006.2.a.d 1
2006.2.a.e 1
2006.2.a.f 1
2006.2.a.g 1
2006.2.a.h 1
2006.2.a.i 1
2006.2.a.j 1
2006.2.a.k 1
2006.2.a.l 2
2006.2.a.m 2
2006.2.a.n 3
2006.2.a.o 3
2006.2.a.p 4
2006.2.a.q 4
2006.2.a.r 4
2006.2.a.s 4
2006.2.a.t 8
2006.2.a.u 9
2006.2.a.v 12
2006.2.a.w 13
2006.2.b \(\chi_{2006}(237, \cdot)\) 2006.2.b.a 2 1
2006.2.b.b 2
2006.2.b.c 2
2006.2.b.d 4
2006.2.b.e 4
2006.2.b.f 4
2006.2.b.g 4
2006.2.b.h 4
2006.2.b.i 6
2006.2.b.j 6
2006.2.b.k 6
2006.2.b.l 6
2006.2.b.m 10
2006.2.b.n 10
2006.2.b.o 16
2006.2.f \(\chi_{2006}(591, \cdot)\) n/a 172 2
2006.2.g \(\chi_{2006}(355, \cdot)\) n/a 352 4
2006.2.j \(\chi_{2006}(235, \cdot)\) n/a 720 8
2006.2.k \(\chi_{2006}(35, \cdot)\) n/a 2240 28
2006.2.n \(\chi_{2006}(135, \cdot)\) n/a 2520 28
2006.2.o \(\chi_{2006}(21, \cdot)\) n/a 5040 56
2006.2.r \(\chi_{2006}(9, \cdot)\) n/a 10080 112
2006.2.s \(\chi_{2006}(11, \cdot)\) n/a 20160 224

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2006))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2006)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1003))\)\(^{\oplus 2}\)