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Properties

Label 3872.2
Level 3872
Weight 2
Dimension 255653
Nonzero newspaces 24
Sturm bound 1858560
Trace bound 9

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Defining parameters

Level: \( N \) = \( 3872 = 2^{5} \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(1858560\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3872))\).

Total New Old
Modular forms 469760 258463 211297
Cusp forms 459521 255653 203868
Eisenstein series 10239 2810 7429

Trace form

\( 255653 q - 364 q^{2} - 274 q^{3} - 364 q^{4} - 366 q^{5} - 364 q^{6} - 274 q^{7} - 364 q^{8} - 547 q^{9} + O(q^{10}) \) \( 255653 q - 364 q^{2} - 274 q^{3} - 364 q^{4} - 366 q^{5} - 364 q^{6} - 274 q^{7} - 364 q^{8} - 547 q^{9} - 356 q^{10} - 300 q^{11} - 668 q^{12} - 358 q^{13} - 348 q^{14} - 270 q^{15} - 344 q^{16} - 178 q^{17} - 344 q^{18} - 274 q^{19} - 348 q^{20} - 364 q^{21} - 400 q^{22} - 506 q^{23} - 376 q^{24} - 545 q^{25} - 384 q^{26} - 250 q^{27} - 384 q^{28} - 374 q^{29} - 396 q^{30} - 254 q^{31} - 384 q^{32} - 1000 q^{33} - 696 q^{34} - 250 q^{35} - 392 q^{36} - 366 q^{37} - 356 q^{38} - 250 q^{39} - 352 q^{40} - 534 q^{41} - 344 q^{42} - 246 q^{43} - 400 q^{44} - 666 q^{45} - 332 q^{46} - 270 q^{47} - 312 q^{48} - 187 q^{49} - 324 q^{50} - 278 q^{51} - 356 q^{52} - 334 q^{53} - 352 q^{54} - 300 q^{55} - 672 q^{56} - 544 q^{57} - 368 q^{58} - 306 q^{59} - 368 q^{60} - 342 q^{61} - 384 q^{62} - 258 q^{63} - 400 q^{64} - 920 q^{65} - 400 q^{66} - 554 q^{67} - 344 q^{68} - 332 q^{69} - 376 q^{70} - 266 q^{71} - 340 q^{72} - 390 q^{73} - 348 q^{74} - 126 q^{75} - 364 q^{76} - 320 q^{77} - 644 q^{78} - 70 q^{79} - 368 q^{80} + 69 q^{81} - 364 q^{82} - 34 q^{83} - 344 q^{84} - 28 q^{85} - 384 q^{86} + 2 q^{87} - 400 q^{88} - 854 q^{89} - 352 q^{90} + 14 q^{91} - 400 q^{92} - 56 q^{93} - 352 q^{94} - 14 q^{95} - 360 q^{96} - 650 q^{97} - 384 q^{98} - 200 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3872))\)

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
3872.2.a \(\chi_{3872}(1, \cdot)\) 3872.2.a.a 1 1
3872.2.a.b 1
3872.2.a.c 1
3872.2.a.d 1
3872.2.a.e 1
3872.2.a.f 1
3872.2.a.g 1
3872.2.a.h 1
3872.2.a.i 1
3872.2.a.j 1
3872.2.a.k 1
3872.2.a.l 1
3872.2.a.m 1
3872.2.a.n 2
3872.2.a.o 2
3872.2.a.p 2
3872.2.a.q 2
3872.2.a.r 2
3872.2.a.s 2
3872.2.a.t 2
3872.2.a.u 2
3872.2.a.v 2
3872.2.a.w 2
3872.2.a.x 2
3872.2.a.y 2
3872.2.a.z 2
3872.2.a.ba 2
3872.2.a.bb 3
3872.2.a.bc 3
3872.2.a.bd 3
3872.2.a.be 3
3872.2.a.bf 4
3872.2.a.bg 4
3872.2.a.bh 4
3872.2.a.bi 4
3872.2.a.bj 4
3872.2.a.bk 4
3872.2.a.bl 4
3872.2.a.bm 4
3872.2.a.bn 6
3872.2.a.bo 6
3872.2.a.bp 6
3872.2.a.bq 6
3872.2.c \(\chi_{3872}(1937, \cdot)\) 3872.2.c.a 2 1
3872.2.c.b 4
3872.2.c.c 8
3872.2.c.d 10
3872.2.c.e 10
3872.2.c.f 10
3872.2.c.g 16
3872.2.c.h 20
3872.2.c.i 20
3872.2.e \(\chi_{3872}(3871, \cdot)\) n/a 108 1
3872.2.g \(\chi_{3872}(1935, \cdot)\) 3872.2.g.a 8 1
3872.2.g.b 8
3872.2.g.c 20
3872.2.g.d 32
3872.2.g.e 32
3872.2.i \(\chi_{3872}(967, \cdot)\) None 0 2
3872.2.j \(\chi_{3872}(969, \cdot)\) None 0 2
3872.2.m \(\chi_{3872}(1697, \cdot)\) n/a 432 4
3872.2.n \(\chi_{3872}(485, \cdot)\) n/a 1708 4
3872.2.q \(\chi_{3872}(483, \cdot)\) n/a 1696 4
3872.2.s \(\chi_{3872}(239, \cdot)\) n/a 400 4
3872.2.u \(\chi_{3872}(959, \cdot)\) n/a 432 4
3872.2.w \(\chi_{3872}(81, \cdot)\) n/a 400 4
3872.2.y \(\chi_{3872}(353, \cdot)\) n/a 1320 10
3872.2.bb \(\chi_{3872}(9, \cdot)\) None 0 8
3872.2.bc \(\chi_{3872}(215, \cdot)\) None 0 8
3872.2.bd \(\chi_{3872}(351, \cdot)\) n/a 1320 10
3872.2.bf \(\chi_{3872}(177, \cdot)\) n/a 1300 10
3872.2.bi \(\chi_{3872}(175, \cdot)\) n/a 1300 10
3872.2.bk \(\chi_{3872}(403, \cdot)\) n/a 6784 16
3872.2.bn \(\chi_{3872}(245, \cdot)\) n/a 6784 16
3872.2.bq \(\chi_{3872}(89, \cdot)\) None 0 20
3872.2.br \(\chi_{3872}(87, \cdot)\) None 0 20
3872.2.bs \(\chi_{3872}(97, \cdot)\) n/a 5280 40
3872.2.bt \(\chi_{3872}(43, \cdot)\) n/a 21040 40
3872.2.bw \(\chi_{3872}(45, \cdot)\) n/a 21040 40
3872.2.by \(\chi_{3872}(79, \cdot)\) n/a 5200 40
3872.2.cb \(\chi_{3872}(49, \cdot)\) n/a 5200 40
3872.2.cd \(\chi_{3872}(63, \cdot)\) n/a 5280 40
3872.2.ce \(\chi_{3872}(7, \cdot)\) None 0 80
3872.2.cf \(\chi_{3872}(25, \cdot)\) None 0 80
3872.2.ci \(\chi_{3872}(5, \cdot)\) n/a 84160 160
3872.2.cl \(\chi_{3872}(19, \cdot)\) n/a 84160 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3872))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3872)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(968))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1936))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3872))\)\(^{\oplus 1}\)