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Properties

Label 1692.2
Level 1692
Weight 2
Dimension 36268
Nonzero newspaces 16
Sturm bound 317952
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1692 = 2^{2} \cdot 3^{2} \cdot 47 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(317952\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1692))\).

Total New Old
Modular forms 81328 37080 44248
Cusp forms 77649 36268 41381
Eisenstein series 3679 812 2867

Trace form

\( 36268 q - 63 q^{2} - 59 q^{4} - 120 q^{5} - 86 q^{6} + 6 q^{7} - 69 q^{8} - 160 q^{9} + O(q^{10}) \) \( 36268 q - 63 q^{2} - 59 q^{4} - 120 q^{5} - 86 q^{6} + 6 q^{7} - 69 q^{8} - 160 q^{9} - 199 q^{10} + 6 q^{11} - 104 q^{12} - 124 q^{13} - 93 q^{14} - 18 q^{15} - 83 q^{16} - 162 q^{17} - 128 q^{18} - 105 q^{20} - 178 q^{21} - 75 q^{22} - 6 q^{23} - 98 q^{24} - 120 q^{25} - 69 q^{26} - 183 q^{28} - 144 q^{29} - 56 q^{30} + 18 q^{31} - 3 q^{32} - 214 q^{33} - 43 q^{34} - 11 q^{35} - 26 q^{36} - 417 q^{37} - 15 q^{38} + 6 q^{39} - 73 q^{40} - 249 q^{41} - 56 q^{42} - 41 q^{43} - 69 q^{44} - 214 q^{45} - 208 q^{46} - 55 q^{47} - 226 q^{48} - 222 q^{49} - 111 q^{50} - 133 q^{52} - 137 q^{53} - 170 q^{54} - 105 q^{55} - 105 q^{56} - 196 q^{57} - 133 q^{58} - 29 q^{59} - 104 q^{60} - 171 q^{61} - 69 q^{62} + 6 q^{63} - 227 q^{64} - 84 q^{65} - 44 q^{66} + 18 q^{67} - 39 q^{68} - 106 q^{69} - 57 q^{70} + 48 q^{71} - 50 q^{72} - 298 q^{73} - 9 q^{74} + 24 q^{75} - 17 q^{76} - 38 q^{77} - 68 q^{78} + 122 q^{79} + 92 q^{80} - 160 q^{81} - 28 q^{82} + 28 q^{83} - 152 q^{84} + 26 q^{85} + 73 q^{86} + 18 q^{87} + 249 q^{88} - 70 q^{89} - 104 q^{90} + 242 q^{91} + 90 q^{92} - 274 q^{93} + 225 q^{94} + 160 q^{95} - 116 q^{96} - 92 q^{97} + 138 q^{98} - 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1692))\)

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
1692.2.a \(\chi_{1692}(1, \cdot)\) 1692.2.a.a 1 1
1692.2.a.b 1
1692.2.a.c 1
1692.2.a.d 1
1692.2.a.e 2
1692.2.a.f 2
1692.2.a.g 2
1692.2.a.h 2
1692.2.a.i 3
1692.2.a.j 3
1692.2.b \(\chi_{1692}(1315, \cdot)\) n/a 118 1
1692.2.c \(\chi_{1692}(1223, \cdot)\) 1692.2.c.a 2 1
1692.2.c.b 2
1692.2.c.c 44
1692.2.c.d 44
1692.2.h \(\chi_{1692}(845, \cdot)\) 1692.2.h.a 16 1
1692.2.i \(\chi_{1692}(565, \cdot)\) 1692.2.i.a 6 2
1692.2.i.b 40
1692.2.i.c 46
1692.2.j \(\chi_{1692}(281, \cdot)\) 1692.2.j.a 96 2
1692.2.o \(\chi_{1692}(95, \cdot)\) n/a 552 2
1692.2.p \(\chi_{1692}(187, \cdot)\) n/a 568 2
1692.2.q \(\chi_{1692}(37, \cdot)\) n/a 440 22
1692.2.r \(\chi_{1692}(125, \cdot)\) n/a 352 22
1692.2.w \(\chi_{1692}(71, \cdot)\) n/a 2112 22
1692.2.x \(\chi_{1692}(19, \cdot)\) n/a 2596 22
1692.2.y \(\chi_{1692}(25, \cdot)\) n/a 2112 44
1692.2.z \(\chi_{1692}(31, \cdot)\) n/a 12496 44
1692.2.ba \(\chi_{1692}(59, \cdot)\) n/a 12496 44
1692.2.bf \(\chi_{1692}(5, \cdot)\) n/a 2112 44

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1692))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1692)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(94))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(141))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(188))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(282))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(423))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(564))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(846))\)\(^{\oplus 2}\)