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Properties

Label 3376.2
Level 3376
Weight 2
Dimension 199391
Nonzero newspaces 32
Sturm bound 1424640
Trace bound 3

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Defining parameters

Level: \( N \) = \( 3376 = 2^{4} \cdot 211 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(1424640\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3376))\).

Total New Old
Modular forms 359100 201271 157829
Cusp forms 353221 199391 153830
Eisenstein series 5879 1880 3999

Trace form

\( 199391 q - 416 q^{2} - 311 q^{3} - 420 q^{4} - 521 q^{5} - 428 q^{6} - 315 q^{7} - 428 q^{8} - 105 q^{9} + O(q^{10}) \) \( 199391 q - 416 q^{2} - 311 q^{3} - 420 q^{4} - 521 q^{5} - 428 q^{6} - 315 q^{7} - 428 q^{8} - 105 q^{9} - 420 q^{10} - 319 q^{11} - 412 q^{12} - 521 q^{13} - 412 q^{14} - 323 q^{15} - 404 q^{16} - 937 q^{17} - 424 q^{18} - 327 q^{19} - 428 q^{20} - 533 q^{21} - 420 q^{22} - 315 q^{23} - 420 q^{24} - 105 q^{25} - 428 q^{26} - 299 q^{27} - 436 q^{28} - 537 q^{29} - 412 q^{30} - 283 q^{31} - 436 q^{32} - 937 q^{33} - 428 q^{34} - 307 q^{35} - 412 q^{36} - 537 q^{37} - 396 q^{38} - 315 q^{39} - 404 q^{40} - 105 q^{41} - 420 q^{42} - 335 q^{43} - 412 q^{44} - 529 q^{45} - 444 q^{46} - 347 q^{47} - 436 q^{48} - 957 q^{49} - 408 q^{50} - 323 q^{51} - 412 q^{52} - 505 q^{53} - 420 q^{54} - 315 q^{55} - 404 q^{56} - 105 q^{57} - 396 q^{58} - 303 q^{59} - 420 q^{60} - 489 q^{61} - 452 q^{62} - 323 q^{63} - 420 q^{64} - 953 q^{65} - 428 q^{66} - 295 q^{67} - 420 q^{68} - 501 q^{69} - 436 q^{70} - 315 q^{71} - 428 q^{72} - 105 q^{73} - 420 q^{74} - 327 q^{75} - 444 q^{76} - 533 q^{77} - 412 q^{78} - 315 q^{79} - 436 q^{80} - 965 q^{81} - 420 q^{82} - 311 q^{83} - 404 q^{84} - 533 q^{85} - 420 q^{86} - 315 q^{87} - 436 q^{88} - 105 q^{89} - 412 q^{90} - 323 q^{91} - 372 q^{92} - 557 q^{93} - 388 q^{94} - 291 q^{95} - 388 q^{96} - 937 q^{97} - 408 q^{98} - 311 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3376))\)

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
3376.2.a \(\chi_{3376}(1, \cdot)\) 3376.2.a.a 1 1
3376.2.a.b 1
3376.2.a.c 1
3376.2.a.d 1
3376.2.a.e 2
3376.2.a.f 2
3376.2.a.g 2
3376.2.a.h 2
3376.2.a.i 2
3376.2.a.j 3
3376.2.a.k 3
3376.2.a.l 3
3376.2.a.m 3
3376.2.a.n 3
3376.2.a.o 4
3376.2.a.p 5
3376.2.a.q 6
3376.2.a.r 6
3376.2.a.s 9
3376.2.a.t 10
3376.2.a.u 10
3376.2.a.v 12
3376.2.a.w 14
3376.2.b \(\chi_{3376}(1689, \cdot)\) None 0 1
3376.2.c \(\chi_{3376}(1687, \cdot)\) None 0 1
3376.2.h \(\chi_{3376}(3375, \cdot)\) n/a 106 1
3376.2.i \(\chi_{3376}(225, \cdot)\) n/a 210 2
3376.2.j \(\chi_{3376}(843, \cdot)\) n/a 844 2
3376.2.k \(\chi_{3376}(845, \cdot)\) n/a 840 2
3376.2.n \(\chi_{3376}(529, \cdot)\) n/a 420 4
3376.2.q \(\chi_{3376}(15, \cdot)\) n/a 212 2
3376.2.r \(\chi_{3376}(1673, \cdot)\) None 0 2
3376.2.s \(\chi_{3376}(1463, \cdot)\) None 0 2
3376.2.v \(\chi_{3376}(545, \cdot)\) n/a 630 6
3376.2.w \(\chi_{3376}(351, \cdot)\) n/a 424 4
3376.2.bb \(\chi_{3376}(23, \cdot)\) None 0 4
3376.2.bc \(\chi_{3376}(1321, \cdot)\) None 0 4
3376.2.bf \(\chi_{3376}(829, \cdot)\) n/a 1688 4
3376.2.bg \(\chi_{3376}(619, \cdot)\) n/a 1688 4
3376.2.bh \(\chi_{3376}(63, \cdot)\) n/a 636 6
3376.2.bm \(\chi_{3376}(1095, \cdot)\) None 0 6
3376.2.bn \(\chi_{3376}(777, \cdot)\) None 0 6
3376.2.bo \(\chi_{3376}(865, \cdot)\) n/a 840 8
3376.2.br \(\chi_{3376}(477, \cdot)\) n/a 3376 8
3376.2.bs \(\chi_{3376}(315, \cdot)\) n/a 3376 8
3376.2.bt \(\chi_{3376}(161, \cdot)\) n/a 1260 12
3376.2.bw \(\chi_{3376}(269, \cdot)\) n/a 5064 12
3376.2.bx \(\chi_{3376}(67, \cdot)\) n/a 5064 12
3376.2.ca \(\chi_{3376}(823, \cdot)\) None 0 8
3376.2.cb \(\chi_{3376}(137, \cdot)\) None 0 8
3376.2.cc \(\chi_{3376}(111, \cdot)\) n/a 848 8
3376.2.cf \(\chi_{3376}(65, \cdot)\) n/a 2520 24
3376.2.ci \(\chi_{3376}(455, \cdot)\) None 0 12
3376.2.cj \(\chi_{3376}(73, \cdot)\) None 0 12
3376.2.ck \(\chi_{3376}(31, \cdot)\) n/a 1272 12
3376.2.cn \(\chi_{3376}(339, \cdot)\) n/a 6752 16
3376.2.co \(\chi_{3376}(21, \cdot)\) n/a 6752 16
3376.2.cr \(\chi_{3376}(25, \cdot)\) None 0 24
3376.2.cs \(\chi_{3376}(135, \cdot)\) None 0 24
3376.2.cx \(\chi_{3376}(239, \cdot)\) n/a 2544 24
3376.2.cy \(\chi_{3376}(243, \cdot)\) n/a 10128 24
3376.2.cz \(\chi_{3376}(101, \cdot)\) n/a 10128 24
3376.2.dc \(\chi_{3376}(49, \cdot)\) n/a 5040 48
3376.2.dd \(\chi_{3376}(27, \cdot)\) n/a 20256 48
3376.2.de \(\chi_{3376}(5, \cdot)\) n/a 20256 48
3376.2.dj \(\chi_{3376}(127, \cdot)\) n/a 5088 48
3376.2.dk \(\chi_{3376}(9, \cdot)\) None 0 48
3376.2.dl \(\chi_{3376}(7, \cdot)\) None 0 48
3376.2.dq \(\chi_{3376}(37, \cdot)\) n/a 40512 96
3376.2.dr \(\chi_{3376}(3, \cdot)\) n/a 40512 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3376))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3376)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(211))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(422))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(844))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1688))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3376))\)\(^{\oplus 1}\)