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Properties

Label 1005.2
Level 1005
Weight 2
Dimension 24287
Nonzero newspaces 24
Sturm bound 143616
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1005 = 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(143616\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1005))\).

Total New Old
Modular forms 36960 25063 11897
Cusp forms 34849 24287 10562
Eisenstein series 2111 776 1335

Trace form

\( 24287 q + 5 q^{2} - 63 q^{3} - 123 q^{4} - q^{5} - 197 q^{6} - 124 q^{7} + 9 q^{8} - 67 q^{9} + O(q^{10}) \) \( 24287 q + 5 q^{2} - 63 q^{3} - 123 q^{4} - q^{5} - 197 q^{6} - 124 q^{7} + 9 q^{8} - 67 q^{9} - 193 q^{10} + 20 q^{11} - 61 q^{12} - 114 q^{13} + 24 q^{14} - 96 q^{15} - 363 q^{16} + 14 q^{17} - 61 q^{18} - 120 q^{19} + 9 q^{20} - 190 q^{21} - 104 q^{22} + 24 q^{23} - 45 q^{24} - 199 q^{25} + 38 q^{26} - 63 q^{27} - 76 q^{28} + 34 q^{29} - 98 q^{30} - 364 q^{31} + 73 q^{32} - 62 q^{33} - 74 q^{34} + 8 q^{35} - 189 q^{36} - 74 q^{37} + 68 q^{38} - 56 q^{39} - 189 q^{40} + 22 q^{41} - 42 q^{42} - 96 q^{43} + 76 q^{44} - 100 q^{45} - 324 q^{46} + 32 q^{47} - 37 q^{48} - 61 q^{49} + 5 q^{50} - 176 q^{51} - 214 q^{52} - 58 q^{53} - 65 q^{54} - 376 q^{55} - 672 q^{56} - 192 q^{57} - 574 q^{58} - 196 q^{59} - 358 q^{60} - 858 q^{61} - 168 q^{62} - 80 q^{63} - 1339 q^{64} - 246 q^{65} - 748 q^{66} - 341 q^{67} - 398 q^{68} - 174 q^{69} - 702 q^{70} - 440 q^{71} - 321 q^{72} - 650 q^{73} - 170 q^{74} - 228 q^{75} - 1304 q^{76} - 168 q^{77} - 284 q^{78} - 360 q^{79} - 363 q^{80} - 199 q^{81} - 382 q^{82} - 72 q^{83} - 98 q^{84} - 184 q^{85} + 140 q^{86} - 40 q^{87} + 72 q^{88} + 102 q^{89} - 94 q^{90} - 284 q^{91} + 168 q^{92} - 34 q^{93} + 28 q^{94} + 12 q^{95} - 145 q^{96} - 38 q^{97} + 157 q^{98} - 46 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1005))\)

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
1005.2.a \(\chi_{1005}(1, \cdot)\) 1005.2.a.a 1 1
1005.2.a.b 1
1005.2.a.c 4
1005.2.a.d 4
1005.2.a.e 4
1005.2.a.f 4
1005.2.a.g 5
1005.2.a.h 5
1005.2.a.i 7
1005.2.a.j 8
1005.2.c \(\chi_{1005}(604, \cdot)\) 1005.2.c.a 2 1
1005.2.c.b 4
1005.2.c.c 28
1005.2.c.d 34
1005.2.e \(\chi_{1005}(1004, \cdot)\) n/a 132 1
1005.2.g \(\chi_{1005}(401, \cdot)\) 1005.2.g.a 46 1
1005.2.g.b 46
1005.2.i \(\chi_{1005}(766, \cdot)\) 1005.2.i.a 2 2
1005.2.i.b 10
1005.2.i.c 12
1005.2.i.d 22
1005.2.i.e 22
1005.2.i.f 24
1005.2.j \(\chi_{1005}(133, \cdot)\) n/a 136 2
1005.2.k \(\chi_{1005}(68, \cdot)\) n/a 264 2
1005.2.o \(\chi_{1005}(566, \cdot)\) n/a 180 2
1005.2.q \(\chi_{1005}(164, \cdot)\) n/a 264 2
1005.2.s \(\chi_{1005}(364, \cdot)\) n/a 136 2
1005.2.u \(\chi_{1005}(76, \cdot)\) n/a 440 10
1005.2.x \(\chi_{1005}(97, \cdot)\) n/a 272 4
1005.2.y \(\chi_{1005}(632, \cdot)\) n/a 528 4
1005.2.ba \(\chi_{1005}(161, \cdot)\) n/a 920 10
1005.2.bc \(\chi_{1005}(119, \cdot)\) n/a 1320 10
1005.2.be \(\chi_{1005}(64, \cdot)\) n/a 680 10
1005.2.bg \(\chi_{1005}(16, \cdot)\) n/a 920 20
1005.2.bj \(\chi_{1005}(62, \cdot)\) n/a 2640 20
1005.2.bk \(\chi_{1005}(43, \cdot)\) n/a 1360 20
1005.2.bm \(\chi_{1005}(4, \cdot)\) n/a 1360 20
1005.2.bo \(\chi_{1005}(44, \cdot)\) n/a 2640 20
1005.2.bq \(\chi_{1005}(11, \cdot)\) n/a 1800 20
1005.2.bs \(\chi_{1005}(17, \cdot)\) n/a 5280 40
1005.2.bt \(\chi_{1005}(7, \cdot)\) n/a 2720 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(201))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(335))\)\(^{\oplus 2}\)