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Properties

Label 3856.2
Level 3856
Weight 2
Dimension 260276
Nonzero newspaces 52
Sturm bound 1858560
Trace bound 11

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Defining parameters

Level: \( N \) = \( 3856 = 2^{4} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 52 \)
Sturm bound: \(1858560\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3856))\).

Total New Old
Modular forms 468000 262426 205574
Cusp forms 461281 260276 201005
Eisenstein series 6719 2150 4569

Trace form

\( 260276 q - 476 q^{2} - 356 q^{3} - 480 q^{4} - 596 q^{5} - 488 q^{6} - 360 q^{7} - 488 q^{8} - 120 q^{9} + O(q^{10}) \) \( 260276 q - 476 q^{2} - 356 q^{3} - 480 q^{4} - 596 q^{5} - 488 q^{6} - 360 q^{7} - 488 q^{8} - 120 q^{9} - 480 q^{10} - 364 q^{11} - 472 q^{12} - 596 q^{13} - 472 q^{14} - 368 q^{15} - 464 q^{16} - 1072 q^{17} - 484 q^{18} - 372 q^{19} - 488 q^{20} - 608 q^{21} - 480 q^{22} - 360 q^{23} - 480 q^{24} - 120 q^{25} - 488 q^{26} - 344 q^{27} - 496 q^{28} - 612 q^{29} - 472 q^{30} - 328 q^{31} - 496 q^{32} - 1072 q^{33} - 488 q^{34} - 352 q^{35} - 472 q^{36} - 612 q^{37} - 456 q^{38} - 360 q^{39} - 464 q^{40} - 120 q^{41} - 480 q^{42} - 380 q^{43} - 472 q^{44} - 604 q^{45} - 504 q^{46} - 392 q^{47} - 496 q^{48} - 1092 q^{49} - 468 q^{50} - 368 q^{51} - 472 q^{52} - 580 q^{53} - 480 q^{54} - 360 q^{55} - 464 q^{56} - 120 q^{57} - 456 q^{58} - 348 q^{59} - 480 q^{60} - 564 q^{61} - 512 q^{62} - 368 q^{63} - 480 q^{64} - 1088 q^{65} - 488 q^{66} - 340 q^{67} - 480 q^{68} - 576 q^{69} - 496 q^{70} - 360 q^{71} - 488 q^{72} - 120 q^{73} - 480 q^{74} - 372 q^{75} - 504 q^{76} - 608 q^{77} - 472 q^{78} - 360 q^{79} - 496 q^{80} - 1100 q^{81} - 480 q^{82} - 356 q^{83} - 464 q^{84} - 608 q^{85} - 480 q^{86} - 360 q^{87} - 496 q^{88} - 120 q^{89} - 472 q^{90} - 368 q^{91} - 432 q^{92} - 632 q^{93} - 448 q^{94} - 336 q^{95} - 448 q^{96} - 1072 q^{97} - 468 q^{98} - 356 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3856))\)

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
3856.2.a \(\chi_{3856}(1, \cdot)\) 3856.2.a.a 1 1
3856.2.a.b 1
3856.2.a.c 1
3856.2.a.d 1
3856.2.a.e 2
3856.2.a.f 2
3856.2.a.g 3
3856.2.a.h 6
3856.2.a.i 7
3856.2.a.j 7
3856.2.a.k 9
3856.2.a.l 11
3856.2.a.m 12
3856.2.a.n 12
3856.2.a.o 13
3856.2.a.p 13
3856.2.a.q 19
3856.2.b \(\chi_{3856}(2409, \cdot)\) None 0 1
3856.2.c \(\chi_{3856}(1929, \cdot)\) None 0 1
3856.2.h \(\chi_{3856}(481, \cdot)\) n/a 120 1
3856.2.i \(\chi_{3856}(225, \cdot)\) n/a 240 2
3856.2.j \(\chi_{3856}(177, \cdot)\) n/a 240 2
3856.2.m \(\chi_{3856}(965, \cdot)\) n/a 960 2
3856.2.n \(\chi_{3856}(1141, \cdot)\) n/a 964 2
3856.2.q \(\chi_{3856}(1269, \cdot)\) n/a 964 2
3856.2.s \(\chi_{3856}(1445, \cdot)\) n/a 964 2
3856.2.u \(\chi_{3856}(2105, \cdot)\) None 0 2
3856.2.v \(\chi_{3856}(1169, \cdot)\) n/a 480 4
3856.2.y \(\chi_{3856}(257, \cdot)\) n/a 240 2
3856.2.z \(\chi_{3856}(2153, \cdot)\) None 0 2
3856.2.ba \(\chi_{3856}(1913, \cdot)\) None 0 2
3856.2.bd \(\chi_{3856}(693, \cdot)\) n/a 1928 4
3856.2.bh \(\chi_{3856}(753, \cdot)\) n/a 480 4
3856.2.bi \(\chi_{3856}(233, \cdot)\) None 0 4
3856.2.bk \(\chi_{3856}(2621, \cdot)\) n/a 1928 4
3856.2.bl \(\chi_{3856}(625, \cdot)\) n/a 480 4
3856.2.bq \(\chi_{3856}(569, \cdot)\) None 0 4
3856.2.br \(\chi_{3856}(873, \cdot)\) None 0 4
3856.2.bt \(\chi_{3856}(1145, \cdot)\) None 0 4
3856.2.bu \(\chi_{3856}(949, \cdot)\) n/a 1928 4
3856.2.bw \(\chi_{3856}(181, \cdot)\) n/a 1928 4
3856.2.bz \(\chi_{3856}(237, \cdot)\) n/a 1928 4
3856.2.ca \(\chi_{3856}(1189, \cdot)\) n/a 1928 4
3856.2.cc \(\chi_{3856}(1201, \cdot)\) n/a 480 4
3856.2.ce \(\chi_{3856}(401, \cdot)\) n/a 960 8
3856.2.cf \(\chi_{3856}(1731, \cdot)\) n/a 3856 8
3856.2.cg \(\chi_{3856}(111, \cdot)\) n/a 968 8
3856.2.ch \(\chi_{3856}(647, \cdot)\) None 0 8
3856.2.ci \(\chi_{3856}(115, \cdot)\) n/a 3856 8
3856.2.cn \(\chi_{3856}(25, \cdot)\) None 0 8
3856.2.cq \(\chi_{3856}(277, \cdot)\) n/a 3856 8
3856.2.cs \(\chi_{3856}(829, \cdot)\) n/a 3856 8
3856.2.ct \(\chi_{3856}(717, \cdot)\) n/a 3856 8
3856.2.cw \(\chi_{3856}(205, \cdot)\) n/a 3856 8
3856.2.cy \(\chi_{3856}(1681, \cdot)\) n/a 960 8
3856.2.da \(\chi_{3856}(1077, \cdot)\) n/a 3856 8
3856.2.db \(\chi_{3856}(121, \cdot)\) None 0 8
3856.2.dc \(\chi_{3856}(113, \cdot)\) n/a 960 8
3856.2.df \(\chi_{3856}(725, \cdot)\) n/a 3856 8
3856.2.dj \(\chi_{3856}(217, \cdot)\) None 0 8
3856.2.dk \(\chi_{3856}(265, \cdot)\) None 0 8
3856.2.dl \(\chi_{3856}(81, \cdot)\) n/a 960 8
3856.2.do \(\chi_{3856}(5, \cdot)\) n/a 7712 16
3856.2.ds \(\chi_{3856}(41, \cdot)\) None 0 16
3856.2.dt \(\chi_{3856}(193, \cdot)\) n/a 1920 16
3856.2.dv \(\chi_{3856}(61, \cdot)\) n/a 7712 16
3856.2.ea \(\chi_{3856}(11, \cdot)\) n/a 7712 16
3856.2.eb \(\chi_{3856}(63, \cdot)\) n/a 1936 16
3856.2.ec \(\chi_{3856}(263, \cdot)\) None 0 16
3856.2.ed \(\chi_{3856}(19, \cdot)\) n/a 7712 16
3856.2.ef \(\chi_{3856}(97, \cdot)\) n/a 1920 16
3856.2.eg \(\chi_{3856}(341, \cdot)\) n/a 7712 16
3856.2.ej \(\chi_{3856}(565, \cdot)\) n/a 7712 16
3856.2.ek \(\chi_{3856}(813, \cdot)\) n/a 7712 16
3856.2.em \(\chi_{3856}(141, \cdot)\) n/a 7712 16
3856.2.eo \(\chi_{3856}(9, \cdot)\) None 0 16
3856.2.eq \(\chi_{3856}(267, \cdot)\) n/a 15424 32
3856.2.er \(\chi_{3856}(23, \cdot)\) None 0 32
3856.2.es \(\chi_{3856}(575, \cdot)\) n/a 3872 32
3856.2.et \(\chi_{3856}(43, \cdot)\) n/a 15424 32
3856.2.ez \(\chi_{3856}(29, \cdot)\) n/a 15424 32
3856.2.fa \(\chi_{3856}(49, \cdot)\) n/a 3840 32
3856.2.fb \(\chi_{3856}(169, \cdot)\) None 0 32
3856.2.fe \(\chi_{3856}(45, \cdot)\) n/a 15424 32
3856.2.fk \(\chi_{3856}(51, \cdot)\) n/a 30848 64
3856.2.fl \(\chi_{3856}(7, \cdot)\) None 0 64
3856.2.fm \(\chi_{3856}(31, \cdot)\) n/a 7744 64
3856.2.fn \(\chi_{3856}(35, \cdot)\) n/a 30848 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3856))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3856)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(241))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(482))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(964))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1928))\)\(^{\oplus 2}\)