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

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

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

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