Properties

Label 1025.2
Level 1025
Weight 2
Dimension 37866
Nonzero newspaces 56
Sturm bound 168000
Trace bound 10

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Defining parameters

Level: \( N \) = \( 1025 = 5^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(168000\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1025))\).

Total New Old
Modular forms 43120 39464 3656
Cusp forms 40881 37866 3015
Eisenstein series 2239 1598 641

Trace form

\( 37866 q - 246 q^{2} - 248 q^{3} - 254 q^{4} - 310 q^{5} - 408 q^{6} - 256 q^{7} - 270 q^{8} - 266 q^{9} + O(q^{10}) \) \( 37866 q - 246 q^{2} - 248 q^{3} - 254 q^{4} - 310 q^{5} - 408 q^{6} - 256 q^{7} - 270 q^{8} - 266 q^{9} - 330 q^{10} - 408 q^{11} - 296 q^{12} - 268 q^{13} - 288 q^{14} - 340 q^{15} - 414 q^{16} - 256 q^{17} - 268 q^{18} - 240 q^{19} - 300 q^{20} - 408 q^{21} - 232 q^{22} - 248 q^{23} - 220 q^{24} - 290 q^{25} - 808 q^{26} - 260 q^{27} - 232 q^{28} - 260 q^{29} - 340 q^{30} - 428 q^{31} - 366 q^{32} - 356 q^{33} - 348 q^{34} - 360 q^{35} - 594 q^{36} - 366 q^{37} - 340 q^{38} - 352 q^{39} - 350 q^{40} - 444 q^{41} - 652 q^{42} - 268 q^{43} - 388 q^{44} - 270 q^{45} - 448 q^{46} - 316 q^{47} - 328 q^{48} - 284 q^{49} - 270 q^{50} - 848 q^{51} - 286 q^{52} - 278 q^{53} - 260 q^{54} - 340 q^{55} - 440 q^{56} - 240 q^{57} - 280 q^{58} - 260 q^{59} - 300 q^{60} - 428 q^{61} - 212 q^{62} - 268 q^{63} - 274 q^{64} - 330 q^{65} - 536 q^{66} - 356 q^{67} - 352 q^{68} - 372 q^{69} - 380 q^{70} - 528 q^{71} - 470 q^{72} - 388 q^{73} - 368 q^{74} - 340 q^{75} - 1120 q^{76} - 352 q^{77} - 516 q^{78} - 400 q^{79} - 330 q^{80} - 664 q^{81} - 496 q^{82} - 528 q^{83} - 568 q^{84} - 250 q^{85} - 608 q^{86} - 300 q^{87} - 400 q^{88} - 250 q^{89} - 270 q^{90} - 568 q^{91} - 416 q^{92} - 316 q^{93} - 388 q^{94} - 340 q^{95} - 648 q^{96} - 236 q^{97} - 362 q^{98} - 352 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1025))\)

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
1025.2.a \(\chi_{1025}(1, \cdot)\) 1025.2.a.a 1 1
1025.2.a.b 1
1025.2.a.c 1
1025.2.a.d 2
1025.2.a.e 2
1025.2.a.f 2
1025.2.a.g 2
1025.2.a.h 3
1025.2.a.i 3
1025.2.a.j 3
1025.2.a.k 5
1025.2.a.l 5
1025.2.a.m 6
1025.2.a.n 7
1025.2.a.o 7
1025.2.a.p 14
1025.2.b \(\chi_{1025}(124, \cdot)\) 1025.2.b.a 2 1
1025.2.b.b 2
1025.2.b.c 2
1025.2.b.d 4
1025.2.b.e 4
1025.2.b.f 4
1025.2.b.g 6
1025.2.b.h 6
1025.2.b.i 6
1025.2.b.j 10
1025.2.b.k 14
1025.2.c \(\chi_{1025}(1024, \cdot)\) 1025.2.c.a 4 1
1025.2.c.b 4
1025.2.c.c 12
1025.2.c.d 12
1025.2.c.e 28
1025.2.d \(\chi_{1025}(901, \cdot)\) 1025.2.d.a 2 1
1025.2.d.b 2
1025.2.d.c 6
1025.2.d.d 6
1025.2.d.e 14
1025.2.d.f 14
1025.2.d.g 20
1025.2.e \(\chi_{1025}(401, \cdot)\) n/a 126 2
1025.2.j \(\chi_{1025}(524, \cdot)\) n/a 124 2
1025.2.k \(\chi_{1025}(221, \cdot)\) n/a 408 4
1025.2.l \(\chi_{1025}(16, \cdot)\) n/a 408 4
1025.2.m \(\chi_{1025}(206, \cdot)\) n/a 400 4
1025.2.n \(\chi_{1025}(141, \cdot)\) n/a 408 4
1025.2.o \(\chi_{1025}(51, \cdot)\) n/a 256 4
1025.2.p \(\chi_{1025}(346, \cdot)\) n/a 408 4
1025.2.q \(\chi_{1025}(232, \cdot)\) n/a 244 4
1025.2.t \(\chi_{1025}(68, \cdot)\) n/a 244 4
1025.2.u \(\chi_{1025}(209, \cdot)\) n/a 416 4
1025.2.v \(\chi_{1025}(344, \cdot)\) n/a 416 4
1025.2.w \(\chi_{1025}(351, \cdot)\) n/a 256 4
1025.2.x \(\chi_{1025}(646, \cdot)\) n/a 408 4
1025.2.y \(\chi_{1025}(81, \cdot)\) n/a 408 4
1025.2.z \(\chi_{1025}(31, \cdot)\) n/a 408 4
1025.2.ba \(\chi_{1025}(86, \cdot)\) n/a 408 4
1025.2.bb \(\chi_{1025}(174, \cdot)\) n/a 240 4
1025.2.bc \(\chi_{1025}(154, \cdot)\) n/a 416 4
1025.2.bd \(\chi_{1025}(4, \cdot)\) n/a 416 4
1025.2.be \(\chi_{1025}(269, \cdot)\) n/a 416 4
1025.2.bf \(\chi_{1025}(204, \cdot)\) n/a 416 4
1025.2.bg \(\chi_{1025}(329, \cdot)\) n/a 400 4
1025.2.bh \(\chi_{1025}(469, \cdot)\) n/a 416 4
1025.2.bi \(\chi_{1025}(264, \cdot)\) n/a 416 4
1025.2.bj \(\chi_{1025}(59, \cdot)\) n/a 416 4
1025.2.bk \(\chi_{1025}(474, \cdot)\) n/a 240 4
1025.2.bl \(\chi_{1025}(146, \cdot)\) n/a 408 4
1025.2.bm \(\chi_{1025}(121, \cdot)\) n/a 832 8
1025.2.bn \(\chi_{1025}(49, \cdot)\) n/a 496 8
1025.2.bo \(\chi_{1025}(9, \cdot)\) n/a 816 8
1025.2.bp \(\chi_{1025}(84, \cdot)\) n/a 816 8
1025.2.bq \(\chi_{1025}(39, \cdot)\) n/a 816 8
1025.2.br \(\chi_{1025}(244, \cdot)\) n/a 816 8
1025.2.cq \(\chi_{1025}(226, \cdot)\) n/a 504 8
1025.2.cr \(\chi_{1025}(61, \cdot)\) n/a 832 8
1025.2.cs \(\chi_{1025}(21, \cdot)\) n/a 832 8
1025.2.ct \(\chi_{1025}(46, \cdot)\) n/a 832 8
1025.2.cu \(\chi_{1025}(91, \cdot)\) n/a 832 8
1025.2.cv \(\chi_{1025}(144, \cdot)\) n/a 816 8
1025.2.cw \(\chi_{1025}(28, \cdot)\) n/a 1648 16
1025.2.cx \(\chi_{1025}(167, \cdot)\) n/a 1648 16
1025.2.cy \(\chi_{1025}(112, \cdot)\) n/a 1648 16
1025.2.cz \(\chi_{1025}(7, \cdot)\) n/a 976 16
1025.2.da \(\chi_{1025}(58, \cdot)\) n/a 1648 16
1025.2.db \(\chi_{1025}(88, \cdot)\) n/a 1648 16
1025.2.do \(\chi_{1025}(22, \cdot)\) n/a 1648 16
1025.2.dp \(\chi_{1025}(13, \cdot)\) n/a 1648 16
1025.2.dq \(\chi_{1025}(17, \cdot)\) n/a 1648 16
1025.2.dr \(\chi_{1025}(93, \cdot)\) n/a 976 16
1025.2.ds \(\chi_{1025}(3, \cdot)\) n/a 1648 16
1025.2.dt \(\chi_{1025}(12, \cdot)\) n/a 1648 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1025)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(205))\)\(^{\oplus 2}\)