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Properties

Label 2093.2
Level 2093
Weight 2
Dimension 165051
Nonzero newspaces 60
Sturm bound 709632
Trace bound 7

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Defining parameters

Level: \( N \) = \( 2093 = 7 \cdot 13 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(709632\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2093))\).

Total New Old
Modular forms 180576 169667 10909
Cusp forms 174241 165051 9190
Eisenstein series 6335 4616 1719

Trace form

\( 165051 q - 383 q^{2} - 380 q^{3} - 371 q^{4} - 374 q^{5} - 356 q^{6} - 491 q^{7} - 971 q^{8} - 385 q^{9} + O(q^{10}) \) \( 165051 q - 383 q^{2} - 380 q^{3} - 371 q^{4} - 374 q^{5} - 356 q^{6} - 491 q^{7} - 971 q^{8} - 385 q^{9} - 398 q^{10} - 380 q^{11} - 412 q^{12} - 457 q^{13} - 1105 q^{14} - 1000 q^{15} - 467 q^{16} - 418 q^{17} - 583 q^{18} - 456 q^{19} - 574 q^{20} - 596 q^{21} - 1124 q^{22} - 481 q^{23} - 1156 q^{24} - 471 q^{25} - 519 q^{26} - 1028 q^{27} - 657 q^{28} - 1042 q^{29} - 640 q^{30} - 444 q^{31} - 555 q^{32} - 460 q^{33} - 510 q^{34} - 600 q^{35} - 1263 q^{36} - 522 q^{37} - 600 q^{38} - 544 q^{39} - 1242 q^{40} - 534 q^{41} - 854 q^{42} - 1208 q^{43} - 848 q^{44} - 766 q^{45} - 795 q^{46} - 1032 q^{47} - 892 q^{48} - 735 q^{49} - 1381 q^{50} - 664 q^{51} - 799 q^{52} - 990 q^{53} - 880 q^{54} - 704 q^{55} - 915 q^{56} - 1344 q^{57} - 818 q^{58} - 644 q^{59} - 1064 q^{60} - 610 q^{61} - 704 q^{62} - 757 q^{63} - 1443 q^{64} - 752 q^{65} - 1452 q^{66} - 500 q^{67} - 1078 q^{68} - 604 q^{69} - 1438 q^{70} - 1224 q^{71} - 779 q^{72} - 506 q^{73} - 794 q^{74} - 824 q^{75} - 720 q^{76} - 616 q^{77} - 1526 q^{78} - 936 q^{79} - 874 q^{80} - 837 q^{81} - 322 q^{82} - 544 q^{83} - 610 q^{84} - 1124 q^{85} - 740 q^{86} - 608 q^{87} - 212 q^{88} - 482 q^{89} - 710 q^{90} - 501 q^{91} - 2367 q^{92} - 1200 q^{93} - 300 q^{94} - 572 q^{95} - 944 q^{96} - 382 q^{97} - 507 q^{98} - 1428 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2093))\)

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
2093.2.a \(\chi_{2093}(1, \cdot)\) 2093.2.a.a 1 1
2093.2.a.b 1
2093.2.a.c 1
2093.2.a.d 1
2093.2.a.e 1
2093.2.a.f 1
2093.2.a.g 1
2093.2.a.h 1
2093.2.a.i 1
2093.2.a.j 1
2093.2.a.k 2
2093.2.a.l 6
2093.2.a.m 11
2093.2.a.n 15
2093.2.a.o 16
2093.2.a.p 16
2093.2.a.q 16
2093.2.a.r 19
2093.2.a.s 20
2093.2.b \(\chi_{2093}(2092, \cdot)\) n/a 220 1
2093.2.d \(\chi_{2093}(1611, \cdot)\) n/a 156 1
2093.2.g \(\chi_{2093}(482, \cdot)\) n/a 192 1
2093.2.i \(\chi_{2093}(599, \cdot)\) n/a 352 2
2093.2.j \(\chi_{2093}(484, \cdot)\) n/a 304 2
2093.2.k \(\chi_{2093}(737, \cdot)\) n/a 412 2
2093.2.l \(\chi_{2093}(438, \cdot)\) n/a 412 2
2093.2.n \(\chi_{2093}(944, \cdot)\) n/a 416 2
2093.2.p \(\chi_{2093}(827, \cdot)\) n/a 336 2
2093.2.r \(\chi_{2093}(277, \cdot)\) n/a 412 2
2093.2.t \(\chi_{2093}(712, \cdot)\) n/a 440 2
2093.2.u \(\chi_{2093}(367, \cdot)\) n/a 440 2
2093.2.z \(\chi_{2093}(1678, \cdot)\) n/a 384 2
2093.2.bb \(\chi_{2093}(321, \cdot)\) n/a 440 2
2093.2.be \(\chi_{2093}(1011, \cdot)\) n/a 440 2
2093.2.bf \(\chi_{2093}(1128, \cdot)\) n/a 312 2
2093.2.bh \(\chi_{2093}(116, \cdot)\) n/a 408 2
2093.2.bj \(\chi_{2093}(160, \cdot)\) n/a 440 2
2093.2.bl \(\chi_{2093}(1195, \cdot)\) n/a 440 2
2093.2.bo \(\chi_{2093}(576, \cdot)\) n/a 412 2
2093.2.bq \(\chi_{2093}(68, \cdot)\) n/a 440 2
2093.2.bs \(\chi_{2093}(547, \cdot)\) n/a 1440 10
2093.2.bu \(\chi_{2093}(24, \cdot)\) n/a 824 4
2093.2.bv \(\chi_{2093}(137, \cdot)\) n/a 880 4
2093.2.bx \(\chi_{2093}(344, \cdot)\) n/a 672 4
2093.2.by \(\chi_{2093}(1425, \cdot)\) n/a 880 4
2093.2.cb \(\chi_{2093}(691, \cdot)\) n/a 824 4
2093.2.cd \(\chi_{2093}(47, \cdot)\) n/a 816 4
2093.2.ce \(\chi_{2093}(461, \cdot)\) n/a 816 4
2093.2.ci \(\chi_{2093}(436, \cdot)\) n/a 880 4
2093.2.ck \(\chi_{2093}(573, \cdot)\) n/a 1920 10
2093.2.cn \(\chi_{2093}(64, \cdot)\) n/a 1680 10
2093.2.cp \(\chi_{2093}(90, \cdot)\) n/a 2200 10
2093.2.cq \(\chi_{2093}(16, \cdot)\) n/a 4400 20
2093.2.cr \(\chi_{2093}(9, \cdot)\) n/a 4400 20
2093.2.cs \(\chi_{2093}(29, \cdot)\) n/a 3360 20
2093.2.ct \(\chi_{2093}(144, \cdot)\) n/a 3840 20
2093.2.cu \(\chi_{2093}(57, \cdot)\) n/a 3360 20
2093.2.cw \(\chi_{2093}(174, \cdot)\) n/a 4400 20
2093.2.cz \(\chi_{2093}(159, \cdot)\) n/a 4400 20
2093.2.db \(\chi_{2093}(121, \cdot)\) n/a 4400 20
2093.2.de \(\chi_{2093}(38, \cdot)\) n/a 4400 20
2093.2.dg \(\chi_{2093}(153, \cdot)\) n/a 4400 20
2093.2.di \(\chi_{2093}(25, \cdot)\) n/a 4400 20
2093.2.dk \(\chi_{2093}(36, \cdot)\) n/a 3360 20
2093.2.dl \(\chi_{2093}(10, \cdot)\) n/a 4400 20
2093.2.do \(\chi_{2093}(237, \cdot)\) n/a 4400 20
2093.2.dq \(\chi_{2093}(40, \cdot)\) n/a 3840 20
2093.2.dv \(\chi_{2093}(61, \cdot)\) n/a 4400 20
2093.2.dw \(\chi_{2093}(17, \cdot)\) n/a 4400 20
2093.2.dy \(\chi_{2093}(4, \cdot)\) n/a 4400 20
2093.2.ea \(\chi_{2093}(11, \cdot)\) n/a 8800 40
2093.2.ee \(\chi_{2093}(6, \cdot)\) n/a 8800 40
2093.2.ef \(\chi_{2093}(31, \cdot)\) n/a 8800 40
2093.2.eh \(\chi_{2093}(54, \cdot)\) n/a 8800 40
2093.2.ek \(\chi_{2093}(44, \cdot)\) n/a 8800 40
2093.2.el \(\chi_{2093}(15, \cdot)\) n/a 6720 40
2093.2.en \(\chi_{2093}(37, \cdot)\) n/a 8800 40
2093.2.eo \(\chi_{2093}(110, \cdot)\) n/a 8800 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2093))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2093)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(299))\)\(^{\oplus 2}\)