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Properties

Label 1206.2
Level 1206
Weight 2
Dimension 10655
Nonzero newspaces 20
Sturm bound 161568
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1206 = 2 \cdot 3^{2} \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(161568\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1206))\).

Total New Old
Modular forms 41448 10655 30793
Cusp forms 39337 10655 28682
Eisenstein series 2111 0 2111

Trace form

\( 10655 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} + O(q^{10}) \) \( 10655 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} - 6 q^{11} + 4 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + 12 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} - 12 q^{23} + 6 q^{24} - 10 q^{25} - 8 q^{26} - 8 q^{28} + 12 q^{29} - 8 q^{31} + 2 q^{32} + 18 q^{33} - 6 q^{34} - 6 q^{36} + 16 q^{37} - 2 q^{38} + 18 q^{41} - 2 q^{43} + 12 q^{44} + 24 q^{46} - 12 q^{47} - 6 q^{48} - 6 q^{49} - 10 q^{50} - 18 q^{51} + 26 q^{52} + 18 q^{53} - 18 q^{54} + 198 q^{55} + 4 q^{56} - 6 q^{57} + 144 q^{58} + 138 q^{59} + 280 q^{61} + 82 q^{62} + 24 q^{63} - 4 q^{64} + 264 q^{65} + 137 q^{67} + 60 q^{68} + 264 q^{70} + 312 q^{71} - 6 q^{72} + 242 q^{73} + 58 q^{74} + 30 q^{75} + 130 q^{76} + 120 q^{77} + 12 q^{78} + 146 q^{79} + 18 q^{81} + 63 q^{82} + 90 q^{83} + 12 q^{84} - 2 q^{86} - 36 q^{87} - 6 q^{88} - 24 q^{89} - 16 q^{91} - 12 q^{92} - 12 q^{94} + 10 q^{97} + 12 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1206))\)

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
1206.2.a \(\chi_{1206}(1, \cdot)\) 1206.2.a.a 1 1
1206.2.a.b 1
1206.2.a.c 1
1206.2.a.d 1
1206.2.a.e 1
1206.2.a.f 1
1206.2.a.g 2
1206.2.a.h 2
1206.2.a.i 2
1206.2.a.j 2
1206.2.a.k 2
1206.2.a.l 2
1206.2.a.m 3
1206.2.a.n 3
1206.2.a.o 3
1206.2.d \(\chi_{1206}(1205, \cdot)\) 1206.2.d.a 2 1
1206.2.d.b 2
1206.2.d.c 8
1206.2.d.d 8
1206.2.e \(\chi_{1206}(439, \cdot)\) n/a 136 2
1206.2.f \(\chi_{1206}(403, \cdot)\) n/a 132 2
1206.2.g \(\chi_{1206}(565, \cdot)\) n/a 136 2
1206.2.h \(\chi_{1206}(37, \cdot)\) 1206.2.h.a 2 2
1206.2.h.b 4
1206.2.h.c 4
1206.2.h.d 6
1206.2.h.e 6
1206.2.h.f 6
1206.2.h.g 6
1206.2.h.h 12
1206.2.h.i 12
1206.2.k \(\chi_{1206}(365, \cdot)\) n/a 136 2
1206.2.l \(\chi_{1206}(401, \cdot)\) n/a 136 2
1206.2.m \(\chi_{1206}(239, \cdot)\) n/a 136 2
1206.2.t \(\chi_{1206}(1043, \cdot)\) 1206.2.t.a 24 2
1206.2.t.b 24
1206.2.u \(\chi_{1206}(91, \cdot)\) n/a 270 10
1206.2.v \(\chi_{1206}(53, \cdot)\) n/a 200 10
1206.2.y \(\chi_{1206}(19, \cdot)\) n/a 580 20
1206.2.z \(\chi_{1206}(49, \cdot)\) n/a 1360 20
1206.2.ba \(\chi_{1206}(25, \cdot)\) n/a 1360 20
1206.2.bb \(\chi_{1206}(103, \cdot)\) n/a 1360 20
1206.2.bc \(\chi_{1206}(197, \cdot)\) n/a 480 20
1206.2.bj \(\chi_{1206}(41, \cdot)\) n/a 1360 20
1206.2.bk \(\chi_{1206}(5, \cdot)\) n/a 1360 20
1206.2.bl \(\chi_{1206}(11, \cdot)\) n/a 1360 20

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1206))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1206)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(201))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(402))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(603))\)\(^{\oplus 2}\)