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Properties

Label 2052.3
Level 2052
Weight 3
Dimension 106378
Nonzero newspaces 68
Sturm bound 699840
Trace bound 23

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Defining parameters

Level: \( N \) = \( 2052 = 2^{2} \cdot 3^{3} \cdot 19 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 68 \)
Sturm bound: \(699840\)
Trace bound: \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(2052))\).

Total New Old
Modular forms 235980 107466 128514
Cusp forms 230580 106378 124202
Eisenstein series 5400 1088 4312

Trace form

\( 106378 q - 62 q^{2} - 108 q^{4} - 88 q^{5} - 96 q^{6} + 8 q^{7} - 110 q^{8} - 204 q^{9} + O(q^{10}) \) \( 106378 q - 62 q^{2} - 108 q^{4} - 88 q^{5} - 96 q^{6} + 8 q^{7} - 110 q^{8} - 204 q^{9} - 156 q^{10} - 144 q^{11} - 186 q^{12} - 352 q^{13} - 198 q^{14} - 90 q^{15} - 132 q^{16} - 196 q^{17} - 54 q^{18} + 19 q^{19} + 98 q^{20} - 276 q^{21} + 108 q^{22} + 234 q^{23} + 168 q^{24} - 182 q^{25} + 596 q^{26} + 108 q^{28} - 406 q^{29} + 198 q^{30} - 124 q^{31} + 358 q^{32} - 6 q^{33} - 36 q^{34} + 486 q^{35} - 156 q^{36} - 142 q^{37} - 297 q^{38} + 246 q^{39} - 612 q^{40} + 716 q^{41} + 144 q^{42} + 122 q^{43} - 414 q^{44} + 714 q^{45} - 672 q^{46} + 810 q^{47} + 330 q^{48} + 264 q^{49} - 216 q^{50} + 198 q^{51} - 300 q^{52} + 392 q^{53} - 264 q^{54} + 216 q^{55} + 252 q^{56} - 309 q^{57} + 606 q^{58} - 522 q^{59} - 528 q^{60} - 184 q^{61} + 468 q^{62} - 762 q^{63} + 528 q^{64} - 1502 q^{65} - 894 q^{66} - 940 q^{67} - 160 q^{68} - 1266 q^{69} + 156 q^{70} - 1458 q^{71} - 564 q^{72} - 934 q^{73} - 1846 q^{74} - 1194 q^{75} - 741 q^{76} - 2592 q^{77} - 1608 q^{78} - 700 q^{79} - 3364 q^{80} - 564 q^{81} - 1860 q^{82} - 108 q^{83} - 1632 q^{84} - 252 q^{85} - 2178 q^{86} + 882 q^{87} - 564 q^{88} + 434 q^{89} - 1896 q^{90} + 292 q^{91} - 666 q^{92} + 3222 q^{93} + 408 q^{94} - 396 q^{95} - 1164 q^{96} - 754 q^{97} - 2018 q^{98} + 1890 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(2052))\)

We only show spaces with odd 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
2052.3.b \(\chi_{2052}(2051, \cdot)\) n/a 320 1
2052.3.e \(\chi_{2052}(1673, \cdot)\) 2052.3.e.a 12 1
2052.3.e.b 12
2052.3.e.c 24
2052.3.g \(\chi_{2052}(1027, \cdot)\) n/a 288 1
2052.3.h \(\chi_{2052}(1405, \cdot)\) 2052.3.h.a 2 1
2052.3.h.b 24
2052.3.h.c 28
2052.3.m \(\chi_{2052}(881, \cdot)\) 2052.3.m.a 80 2
2052.3.p \(\chi_{2052}(1475, \cdot)\) n/a 472 2
2052.3.q \(\chi_{2052}(163, \cdot)\) n/a 640 2
2052.3.s \(\chi_{2052}(829, \cdot)\) 2052.3.s.a 80 2
2052.3.t \(\chi_{2052}(37, \cdot)\) 2052.3.t.a 80 2
2052.3.v \(\chi_{2052}(343, \cdot)\) n/a 432 2
2052.3.x \(\chi_{2052}(235, \cdot)\) n/a 472 2
2052.3.y \(\chi_{2052}(217, \cdot)\) n/a 108 2
2052.3.ba \(\chi_{2052}(107, \cdot)\) n/a 640 2
2052.3.bc \(\chi_{2052}(305, \cdot)\) 2052.3.bc.a 72 2
2052.3.be \(\chi_{2052}(125, \cdot)\) 2052.3.be.a 80 2
2052.3.bf \(\chi_{2052}(179, \cdot)\) n/a 472 2
2052.3.bh \(\chi_{2052}(683, \cdot)\) n/a 472 2
2052.3.bj \(\chi_{2052}(809, \cdot)\) n/a 108 2
2052.3.bl \(\chi_{2052}(145, \cdot)\) 2052.3.bl.a 80 2
2052.3.bm \(\chi_{2052}(1531, \cdot)\) n/a 472 2
2052.3.cb \(\chi_{2052}(155, \cdot)\) n/a 4296 6
2052.3.cc \(\chi_{2052}(365, \cdot)\) n/a 720 6
2052.3.ce \(\chi_{2052}(421, \cdot)\) n/a 720 6
2052.3.cg \(\chi_{2052}(43, \cdot)\) n/a 4296 6
2052.3.ch \(\chi_{2052}(13, \cdot)\) n/a 720 6
2052.3.cj \(\chi_{2052}(511, \cdot)\) n/a 4296 6
2052.3.ck \(\chi_{2052}(395, \cdot)\) n/a 1416 6
2052.3.cn \(\chi_{2052}(199, \cdot)\) n/a 1416 6
2052.3.cp \(\chi_{2052}(17, \cdot)\) n/a 240 6
2052.3.cq \(\chi_{2052}(109, \cdot)\) n/a 318 6
2052.3.cr \(\chi_{2052}(161, \cdot)\) n/a 318 6
2052.3.ct \(\chi_{2052}(181, \cdot)\) n/a 240 6
2052.3.cu \(\chi_{2052}(59, \cdot)\) n/a 4296 6
2052.3.cv \(\chi_{2052}(193, \cdot)\) n/a 720 6
2052.3.cy \(\chi_{2052}(473, \cdot)\) n/a 720 6
2052.3.cz \(\chi_{2052}(283, \cdot)\) n/a 4296 6
2052.3.db \(\chi_{2052}(5, \cdot)\) n/a 720 6
2052.3.dc \(\chi_{2052}(655, \cdot)\) n/a 4296 6
2052.3.df \(\chi_{2052}(407, \cdot)\) n/a 4296 6
2052.3.dg \(\chi_{2052}(353, \cdot)\) n/a 720 6
2052.3.di \(\chi_{2052}(7, \cdot)\) n/a 4296 6
2052.3.dk \(\chi_{2052}(265, \cdot)\) n/a 720 6
2052.3.dl \(\chi_{2052}(115, \cdot)\) n/a 3888 6
2052.3.dn \(\chi_{2052}(445, \cdot)\) n/a 720 6
2052.3.do \(\chi_{2052}(425, \cdot)\) n/a 720 6
2052.3.dr \(\chi_{2052}(227, \cdot)\) n/a 4296 6
2052.3.ds \(\chi_{2052}(77, \cdot)\) n/a 648 6
2052.3.dv \(\chi_{2052}(335, \cdot)\) n/a 4296 6
2052.3.dw \(\chi_{2052}(373, \cdot)\) n/a 720 6
2052.3.dx \(\chi_{2052}(463, \cdot)\) n/a 4296 6
2052.3.eb \(\chi_{2052}(205, \cdot)\) n/a 720 6
2052.3.ec \(\chi_{2052}(371, \cdot)\) n/a 4296 6
2052.3.ef \(\chi_{2052}(553, \cdot)\) n/a 720 6
2052.3.eg \(\chi_{2052}(383, \cdot)\) n/a 4296 6
2052.3.ei \(\chi_{2052}(403, \cdot)\) n/a 4296 6
2052.3.ej \(\chi_{2052}(101, \cdot)\) n/a 720 6
2052.3.ek \(\chi_{2052}(415, \cdot)\) n/a 1416 6
2052.3.em \(\chi_{2052}(431, \cdot)\) n/a 1920 6
2052.3.ep \(\chi_{2052}(55, \cdot)\) n/a 1920 6
2052.3.er \(\chi_{2052}(71, \cdot)\) n/a 1416 6
2052.3.es \(\chi_{2052}(469, \cdot)\) n/a 240 6
2052.3.et \(\chi_{2052}(557, \cdot)\) n/a 240 6
2052.3.ew \(\chi_{2052}(245, \cdot)\) n/a 720 6
2052.3.ex \(\chi_{2052}(167, \cdot)\) n/a 4296 6
2052.3.fa \(\chi_{2052}(617, \cdot)\) n/a 720 6
2052.3.fb \(\chi_{2052}(515, \cdot)\) n/a 4296 6
2052.3.fd \(\chi_{2052}(139, \cdot)\) n/a 4296 6
2052.3.ff \(\chi_{2052}(97, \cdot)\) n/a 720 6

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(2052))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(2052)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(513))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(684))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1026))\)\(^{\oplus 2}\)