Properties

Label 2005.2
Level 2005
Weight 2
Dimension 146199
Nonzero newspaces 30
Sturm bound 643200
Trace bound 22

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Defining parameters

Level: \( N \) = \( 2005 = 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(643200\)
Trace bound: \(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2005))\).

Total New Old
Modular forms 162400 148595 13805
Cusp forms 159201 146199 13002
Eisenstein series 3199 2396 803

Trace form

\( 146199 q - 403 q^{2} - 404 q^{3} - 407 q^{4} - 601 q^{5} - 1212 q^{6} - 408 q^{7} - 415 q^{8} - 413 q^{9} + O(q^{10}) \) \( 146199 q - 403 q^{2} - 404 q^{3} - 407 q^{4} - 601 q^{5} - 1212 q^{6} - 408 q^{7} - 415 q^{8} - 413 q^{9} - 603 q^{10} - 1212 q^{11} - 428 q^{12} - 414 q^{13} - 424 q^{14} - 604 q^{15} - 1231 q^{16} - 418 q^{17} - 439 q^{18} - 420 q^{19} - 607 q^{20} - 1232 q^{21} - 436 q^{22} - 424 q^{23} - 460 q^{24} - 601 q^{25} - 1242 q^{26} - 440 q^{27} - 456 q^{28} - 430 q^{29} - 612 q^{30} - 1232 q^{31} - 463 q^{32} - 448 q^{33} - 454 q^{34} - 608 q^{35} - 1291 q^{36} - 438 q^{37} - 460 q^{38} - 456 q^{39} - 615 q^{40} - 1242 q^{41} - 496 q^{42} - 444 q^{43} - 484 q^{44} - 613 q^{45} - 1272 q^{46} - 448 q^{47} - 524 q^{48} - 457 q^{49} - 603 q^{50} - 1272 q^{51} - 498 q^{52} - 454 q^{53} - 520 q^{54} - 612 q^{55} - 1320 q^{56} - 480 q^{57} - 490 q^{58} - 460 q^{59} - 628 q^{60} - 1262 q^{61} - 496 q^{62} - 504 q^{63} - 527 q^{64} - 614 q^{65} - 1344 q^{66} - 468 q^{67} - 526 q^{68} - 496 q^{69} - 624 q^{70} - 1272 q^{71} - 595 q^{72} - 474 q^{73} - 514 q^{74} - 604 q^{75} - 1340 q^{76} - 496 q^{77} - 568 q^{78} - 480 q^{79} - 631 q^{80} - 1321 q^{81} - 526 q^{82} - 484 q^{83} - 624 q^{84} - 618 q^{85} - 1332 q^{86} - 520 q^{87} - 580 q^{88} - 490 q^{89} - 639 q^{90} - 1312 q^{91} - 568 q^{92} - 528 q^{93} - 544 q^{94} - 620 q^{95} - 1452 q^{96} - 498 q^{97} - 571 q^{98} - 556 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2005))\)

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
2005.2.a \(\chi_{2005}(1, \cdot)\) 2005.2.a.a 1 1
2005.2.a.b 1
2005.2.a.c 3
2005.2.a.d 25
2005.2.a.e 29
2005.2.a.f 37
2005.2.a.g 37
2005.2.b \(\chi_{2005}(1204, \cdot)\) n/a 200 1
2005.2.c \(\chi_{2005}(2004, \cdot)\) n/a 200 1
2005.2.d \(\chi_{2005}(801, \cdot)\) n/a 134 1
2005.2.e \(\chi_{2005}(381, \cdot)\) n/a 268 2
2005.2.j \(\chi_{2005}(1584, \cdot)\) n/a 400 2
2005.2.k \(\chi_{2005}(841, \cdot)\) n/a 536 4
2005.2.m \(\chi_{2005}(356, \cdot)\) n/a 536 4
2005.2.n \(\chi_{2005}(499, \cdot)\) n/a 792 4
2005.2.p \(\chi_{2005}(831, \cdot)\) n/a 536 4
2005.2.q \(\chi_{2005}(29, \cdot)\) n/a 800 4
2005.2.r \(\chi_{2005}(39, \cdot)\) n/a 800 4
2005.2.u \(\chi_{2005}(147, \cdot)\) n/a 1592 8
2005.2.v \(\chi_{2005}(133, \cdot)\) n/a 1592 8
2005.2.w \(\chi_{2005}(164, \cdot)\) n/a 1600 8
2005.2.bb \(\chi_{2005}(56, \cdot)\) n/a 1072 8
2005.2.bc \(\chi_{2005}(51, \cdot)\) n/a 2680 20
2005.2.be \(\chi_{2005}(114, \cdot)\) n/a 3168 16
2005.2.bf \(\chi_{2005}(126, \cdot)\) n/a 2144 16
2005.2.bh \(\chi_{2005}(16, \cdot)\) n/a 2680 20
2005.2.bi \(\chi_{2005}(224, \cdot)\) n/a 4000 20
2005.2.bj \(\chi_{2005}(14, \cdot)\) n/a 4000 20
2005.2.bk \(\chi_{2005}(48, \cdot)\) n/a 6368 32
2005.2.bl \(\chi_{2005}(33, \cdot)\) n/a 6368 32
2005.2.bo \(\chi_{2005}(81, \cdot)\) n/a 5360 40
2005.2.bt \(\chi_{2005}(4, \cdot)\) n/a 8000 40
2005.2.bu \(\chi_{2005}(9, \cdot)\) n/a 15840 80
2005.2.bx \(\chi_{2005}(11, \cdot)\) n/a 10720 80
2005.2.by \(\chi_{2005}(12, \cdot)\) n/a 31840 160
2005.2.cb \(\chi_{2005}(3, \cdot)\) n/a 31840 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(401))\)\(^{\oplus 2}\)