Properties

Label 1145.2
Level 1145
Weight 2
Dimension 47385
Nonzero newspaces 24
Sturm bound 209760
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1145 = 5 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(209760\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1145))\).

Total New Old
Modular forms 53352 48749 4603
Cusp forms 51529 47385 4144
Eisenstein series 1823 1364 459

Trace form

\( 47385 q - 231 q^{2} - 232 q^{3} - 235 q^{4} - 343 q^{5} - 696 q^{6} - 236 q^{7} - 243 q^{8} - 241 q^{9} + O(q^{10}) \) \( 47385 q - 231 q^{2} - 232 q^{3} - 235 q^{4} - 343 q^{5} - 696 q^{6} - 236 q^{7} - 243 q^{8} - 241 q^{9} - 345 q^{10} - 696 q^{11} - 256 q^{12} - 242 q^{13} - 252 q^{14} - 346 q^{15} - 715 q^{16} - 246 q^{17} - 267 q^{18} - 248 q^{19} - 349 q^{20} - 716 q^{21} - 264 q^{22} - 252 q^{23} - 288 q^{24} - 343 q^{25} - 726 q^{26} - 268 q^{27} - 284 q^{28} - 258 q^{29} - 354 q^{30} - 716 q^{31} - 291 q^{32} - 276 q^{33} - 282 q^{34} - 350 q^{35} - 775 q^{36} - 266 q^{37} - 288 q^{38} - 284 q^{39} - 357 q^{40} - 726 q^{41} - 324 q^{42} - 272 q^{43} - 312 q^{44} - 355 q^{45} - 756 q^{46} - 276 q^{47} - 352 q^{48} - 285 q^{49} - 345 q^{50} - 756 q^{51} - 326 q^{52} - 282 q^{53} - 348 q^{54} - 354 q^{55} - 804 q^{56} - 308 q^{57} - 318 q^{58} - 288 q^{59} - 370 q^{60} - 746 q^{61} - 324 q^{62} - 332 q^{63} - 355 q^{64} - 356 q^{65} - 828 q^{66} - 296 q^{67} - 354 q^{68} - 324 q^{69} - 366 q^{70} - 756 q^{71} - 423 q^{72} - 302 q^{73} - 342 q^{74} - 346 q^{75} - 824 q^{76} - 324 q^{77} - 396 q^{78} - 308 q^{79} - 373 q^{80} - 805 q^{81} - 354 q^{82} - 312 q^{83} - 452 q^{84} - 360 q^{85} - 816 q^{86} - 348 q^{87} - 408 q^{88} - 318 q^{89} - 381 q^{90} - 796 q^{91} - 396 q^{92} - 356 q^{93} - 372 q^{94} - 362 q^{95} - 936 q^{96} - 326 q^{97} - 399 q^{98} - 384 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1145))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1145.2.a \(\chi_{1145}(1, \cdot)\) 1145.2.a.a 1 1
1145.2.a.b 2
1145.2.a.c 15
1145.2.a.d 17
1145.2.a.e 20
1145.2.a.f 22
1145.2.b \(\chi_{1145}(459, \cdot)\) 1145.2.b.a 4 1
1145.2.b.b 4
1145.2.b.c 44
1145.2.b.d 62
1145.2.c \(\chi_{1145}(686, \cdot)\) 1145.2.c.a 38 1
1145.2.c.b 40
1145.2.d \(\chi_{1145}(1144, \cdot)\) n/a 112 1
1145.2.e \(\chi_{1145}(781, \cdot)\) n/a 152 2
1145.2.f \(\chi_{1145}(122, \cdot)\) n/a 226 2
1145.2.k \(\chi_{1145}(107, \cdot)\) n/a 226 2
1145.2.l \(\chi_{1145}(1011, \cdot)\) n/a 152 2
1145.2.m \(\chi_{1145}(94, \cdot)\) n/a 228 2
1145.2.n \(\chi_{1145}(324, \cdot)\) n/a 224 2
1145.2.o \(\chi_{1145}(247, \cdot)\) n/a 452 4
1145.2.t \(\chi_{1145}(18, \cdot)\) n/a 452 4
1145.2.u \(\chi_{1145}(16, \cdot)\) n/a 1404 18
1145.2.v \(\chi_{1145}(4, \cdot)\) n/a 2016 18
1145.2.w \(\chi_{1145}(11, \cdot)\) n/a 1404 18
1145.2.x \(\chi_{1145}(44, \cdot)\) n/a 2052 18
1145.2.y \(\chi_{1145}(51, \cdot)\) n/a 2736 36
1145.2.z \(\chi_{1145}(13, \cdot)\) n/a 4068 36
1145.2.be \(\chi_{1145}(2, \cdot)\) n/a 4068 36
1145.2.bf \(\chi_{1145}(49, \cdot)\) n/a 4032 36
1145.2.bg \(\chi_{1145}(9, \cdot)\) n/a 4104 36
1145.2.bh \(\chi_{1145}(36, \cdot)\) n/a 2736 36
1145.2.bi \(\chi_{1145}(7, \cdot)\) n/a 8136 72
1145.2.bn \(\chi_{1145}(63, \cdot)\) n/a 8136 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1145))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1145)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(229))\)\(^{\oplus 2}\)