Properties

Label 2233.2
Level 2233
Weight 2
Dimension 187103
Nonzero newspaces 48
Sturm bound 806400
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2233 = 7 \cdot 11 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(806400\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2233))\).

Total New Old
Modular forms 204960 191959 13001
Cusp forms 198241 187103 11138
Eisenstein series 6719 4856 1863

Trace form

\( 187103 q - 399 q^{2} - 396 q^{3} - 387 q^{4} - 390 q^{5} - 392 q^{6} - 517 q^{7} - 1015 q^{8} - 409 q^{9} + O(q^{10}) \) \( 187103 q - 399 q^{2} - 396 q^{3} - 387 q^{4} - 390 q^{5} - 392 q^{6} - 517 q^{7} - 1015 q^{8} - 409 q^{9} - 414 q^{10} - 461 q^{11} - 924 q^{12} - 386 q^{13} - 531 q^{14} - 1028 q^{15} - 435 q^{16} - 414 q^{17} - 411 q^{18} - 408 q^{19} - 506 q^{20} - 604 q^{21} - 1267 q^{22} - 972 q^{23} - 784 q^{24} - 547 q^{25} - 602 q^{26} - 576 q^{27} - 739 q^{28} - 1173 q^{29} - 1236 q^{30} - 504 q^{31} - 643 q^{32} - 616 q^{33} - 1066 q^{34} - 638 q^{35} - 1443 q^{36} - 470 q^{37} - 560 q^{38} - 572 q^{39} - 562 q^{40} - 462 q^{41} - 664 q^{42} - 1068 q^{43} - 611 q^{44} - 1114 q^{45} - 732 q^{46} - 516 q^{47} - 944 q^{48} - 729 q^{49} - 1453 q^{50} - 676 q^{51} - 902 q^{52} - 718 q^{53} - 1052 q^{54} - 790 q^{55} - 1587 q^{56} - 1360 q^{57} - 1093 q^{58} - 988 q^{59} - 988 q^{60} - 566 q^{61} - 812 q^{62} - 705 q^{63} - 1423 q^{64} - 528 q^{65} - 432 q^{66} - 1088 q^{67} - 562 q^{68} - 404 q^{69} - 646 q^{70} - 1124 q^{71} - 479 q^{72} - 518 q^{73} - 678 q^{74} - 296 q^{75} - 316 q^{76} - 617 q^{77} - 2384 q^{78} - 440 q^{79} - 774 q^{80} - 473 q^{81} - 434 q^{82} - 540 q^{83} - 556 q^{84} - 1212 q^{85} - 728 q^{86} - 552 q^{87} - 1239 q^{88} - 1078 q^{89} - 854 q^{90} - 686 q^{91} - 1608 q^{92} - 588 q^{93} - 700 q^{94} - 896 q^{95} - 1144 q^{96} - 822 q^{97} - 1115 q^{98} - 1785 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2233))\)

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
2233.2.a \(\chi_{2233}(1, \cdot)\) 2233.2.a.a 1 1
2233.2.a.b 1
2233.2.a.c 2
2233.2.a.d 3
2233.2.a.e 5
2233.2.a.f 8
2233.2.a.g 13
2233.2.a.h 14
2233.2.a.i 16
2233.2.a.j 17
2233.2.a.k 17
2233.2.a.l 21
2233.2.a.m 21
2233.2.b \(\chi_{2233}(1770, \cdot)\) n/a 224 1
2233.2.c \(\chi_{2233}(463, \cdot)\) n/a 152 1
2233.2.h \(\chi_{2233}(2232, \cdot)\) n/a 236 1
2233.2.i \(\chi_{2233}(639, \cdot)\) n/a 376 2
2233.2.k \(\chi_{2233}(505, \cdot)\) n/a 360 2
2233.2.m \(\chi_{2233}(650, \cdot)\) n/a 400 2
2233.2.n \(\chi_{2233}(610, \cdot)\) n/a 672 4
2233.2.o \(\chi_{2233}(318, \cdot)\) n/a 472 2
2233.2.t \(\chi_{2233}(144, \cdot)\) n/a 400 2
2233.2.u \(\chi_{2233}(1132, \cdot)\) n/a 448 2
2233.2.v \(\chi_{2233}(78, \cdot)\) n/a 888 6
2233.2.w \(\chi_{2233}(811, \cdot)\) n/a 944 4
2233.2.bb \(\chi_{2233}(1072, \cdot)\) n/a 720 4
2233.2.bc \(\chi_{2233}(349, \cdot)\) n/a 896 4
2233.2.be \(\chi_{2233}(12, \cdot)\) n/a 800 4
2233.2.bg \(\chi_{2233}(186, \cdot)\) n/a 944 4
2233.2.bh \(\chi_{2233}(615, \cdot)\) n/a 1416 6
2233.2.bm \(\chi_{2233}(386, \cdot)\) n/a 912 6
2233.2.bn \(\chi_{2233}(384, \cdot)\) n/a 1416 6
2233.2.bo \(\chi_{2233}(291, \cdot)\) n/a 1792 8
2233.2.bp \(\chi_{2233}(104, \cdot)\) n/a 1888 8
2233.2.br \(\chi_{2233}(162, \cdot)\) n/a 1440 8
2233.2.bt \(\chi_{2233}(23, \cdot)\) n/a 2400 12
2233.2.bu \(\chi_{2233}(188, \cdot)\) n/a 2400 12
2233.2.bw \(\chi_{2233}(43, \cdot)\) n/a 2160 12
2233.2.by \(\chi_{2233}(117, \cdot)\) n/a 1792 8
2233.2.bz \(\chi_{2233}(86, \cdot)\) n/a 1888 8
2233.2.ce \(\chi_{2233}(173, \cdot)\) n/a 1888 8
2233.2.cf \(\chi_{2233}(36, \cdot)\) n/a 4320 24
2233.2.cg \(\chi_{2233}(54, \cdot)\) n/a 2832 12
2233.2.ch \(\chi_{2233}(67, \cdot)\) n/a 2400 12
2233.2.cm \(\chi_{2233}(208, \cdot)\) n/a 2832 12
2233.2.cn \(\chi_{2233}(46, \cdot)\) n/a 3776 16
2233.2.cp \(\chi_{2233}(75, \cdot)\) n/a 3776 16
2233.2.cr \(\chi_{2233}(83, \cdot)\) n/a 5664 24
2233.2.cs \(\chi_{2233}(64, \cdot)\) n/a 4320 24
2233.2.cx \(\chi_{2233}(6, \cdot)\) n/a 5664 24
2233.2.cy \(\chi_{2233}(32, \cdot)\) n/a 5664 24
2233.2.da \(\chi_{2233}(89, \cdot)\) n/a 4800 24
2233.2.dc \(\chi_{2233}(16, \cdot)\) n/a 11328 48
2233.2.de \(\chi_{2233}(8, \cdot)\) n/a 8640 48
2233.2.dg \(\chi_{2233}(27, \cdot)\) n/a 11328 48
2233.2.dh \(\chi_{2233}(96, \cdot)\) n/a 11328 48
2233.2.dm \(\chi_{2233}(4, \cdot)\) n/a 11328 48
2233.2.dn \(\chi_{2233}(24, \cdot)\) n/a 11328 48
2233.2.dp \(\chi_{2233}(3, \cdot)\) n/a 22656 96
2233.2.dr \(\chi_{2233}(2, \cdot)\) n/a 22656 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2233))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2233)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(203))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(319))\)\(^{\oplus 2}\)