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Properties

Label 3328.2
Level 3328
Weight 2
Dimension 190088
Nonzero newspaces 44
Sturm bound 1376256
Trace bound 52

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Defining parameters

Level: \( N \) = \( 3328 = 2^{8} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 44 \)
Sturm bound: \(1376256\)
Trace bound: \(52\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3328))\).

Total New Old
Modular forms 348288 192376 155912
Cusp forms 339841 190088 149753
Eisenstein series 8447 2288 6159

Trace form

\( 190088 q - 320 q^{2} - 240 q^{3} - 320 q^{4} - 320 q^{5} - 320 q^{6} - 240 q^{7} - 320 q^{8} - 400 q^{9} + O(q^{10}) \) \( 190088 q - 320 q^{2} - 240 q^{3} - 320 q^{4} - 320 q^{5} - 320 q^{6} - 240 q^{7} - 320 q^{8} - 400 q^{9} - 320 q^{10} - 240 q^{11} - 320 q^{12} - 352 q^{13} - 704 q^{14} - 240 q^{15} - 320 q^{16} - 480 q^{17} - 320 q^{18} - 240 q^{19} - 320 q^{20} - 320 q^{21} - 320 q^{22} - 240 q^{23} - 320 q^{24} - 400 q^{25} - 352 q^{26} - 528 q^{27} - 320 q^{28} - 320 q^{29} - 320 q^{30} - 224 q^{31} - 320 q^{32} - 560 q^{33} - 320 q^{34} - 240 q^{35} - 320 q^{36} - 320 q^{37} - 320 q^{38} - 264 q^{39} - 704 q^{40} - 400 q^{41} - 320 q^{42} - 240 q^{43} - 320 q^{44} - 272 q^{45} - 320 q^{46} - 240 q^{47} - 320 q^{48} - 424 q^{49} - 320 q^{50} - 176 q^{51} - 352 q^{52} - 640 q^{53} - 320 q^{54} - 112 q^{55} - 320 q^{56} - 272 q^{57} - 320 q^{58} - 112 q^{59} - 320 q^{60} - 192 q^{61} - 320 q^{62} - 96 q^{63} - 320 q^{64} - 728 q^{65} - 704 q^{66} - 80 q^{67} - 320 q^{68} - 192 q^{69} - 320 q^{70} - 112 q^{71} - 320 q^{72} - 272 q^{73} - 320 q^{74} - 112 q^{75} - 320 q^{76} - 256 q^{77} - 352 q^{78} - 464 q^{79} - 320 q^{80} - 408 q^{81} - 320 q^{82} - 240 q^{83} - 320 q^{84} - 240 q^{85} - 320 q^{86} - 240 q^{87} - 320 q^{88} - 400 q^{89} - 320 q^{90} - 264 q^{91} - 704 q^{92} - 416 q^{93} - 320 q^{94} - 224 q^{95} - 320 q^{96} - 560 q^{97} - 320 q^{98} - 192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3328))\)

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
3328.2.a \(\chi_{3328}(1, \cdot)\) 3328.2.a.a 1 1
3328.2.a.b 1
3328.2.a.c 1
3328.2.a.d 1
3328.2.a.e 1
3328.2.a.f 1
3328.2.a.g 1
3328.2.a.h 1
3328.2.a.i 1
3328.2.a.j 1
3328.2.a.k 1
3328.2.a.l 1
3328.2.a.m 2
3328.2.a.n 2
3328.2.a.o 2
3328.2.a.p 2
3328.2.a.q 2
3328.2.a.r 2
3328.2.a.s 2
3328.2.a.t 2
3328.2.a.u 2
3328.2.a.v 2
3328.2.a.w 2
3328.2.a.x 2
3328.2.a.y 2
3328.2.a.z 2
3328.2.a.ba 2
3328.2.a.bb 2
3328.2.a.bc 2
3328.2.a.bd 2
3328.2.a.be 3
3328.2.a.bf 3
3328.2.a.bg 3
3328.2.a.bh 3
3328.2.a.bi 4
3328.2.a.bj 4
3328.2.a.bk 4
3328.2.a.bl 4
3328.2.a.bm 4
3328.2.a.bn 4
3328.2.a.bo 6
3328.2.a.bp 6
3328.2.b \(\chi_{3328}(1665, \cdot)\) 3328.2.b.a 2 1
3328.2.b.b 2
3328.2.b.c 2
3328.2.b.d 2
3328.2.b.e 2
3328.2.b.f 2
3328.2.b.g 2
3328.2.b.h 2
3328.2.b.i 2
3328.2.b.j 2
3328.2.b.k 2
3328.2.b.l 2
3328.2.b.m 2
3328.2.b.n 2
3328.2.b.o 2
3328.2.b.p 2
3328.2.b.q 2
3328.2.b.r 2
3328.2.b.s 2
3328.2.b.t 2
3328.2.b.u 4
3328.2.b.v 4
3328.2.b.w 4
3328.2.b.x 4
3328.2.b.y 4
3328.2.b.z 4
3328.2.b.ba 4
3328.2.b.bb 8
3328.2.b.bc 10
3328.2.b.bd 10
3328.2.e \(\chi_{3328}(129, \cdot)\) n/a 108 1
3328.2.f \(\chi_{3328}(1793, \cdot)\) n/a 108 1
3328.2.i \(\chi_{3328}(1537, \cdot)\) n/a 216 2
3328.2.k \(\chi_{3328}(255, \cdot)\) n/a 216 2
3328.2.l \(\chi_{3328}(447, \cdot)\) n/a 224 2
3328.2.n \(\chi_{3328}(833, \cdot)\) n/a 192 2
3328.2.p \(\chi_{3328}(961, \cdot)\) n/a 224 2
3328.2.s \(\chi_{3328}(2111, \cdot)\) n/a 224 2
3328.2.u \(\chi_{3328}(1919, \cdot)\) n/a 216 2
3328.2.w \(\chi_{3328}(257, \cdot)\) n/a 216 2
3328.2.z \(\chi_{3328}(1153, \cdot)\) n/a 216 2
3328.2.ba \(\chi_{3328}(641, \cdot)\) n/a 216 2
3328.2.bd \(\chi_{3328}(671, \cdot)\) n/a 432 4
3328.2.bf \(\chi_{3328}(417, \cdot)\) n/a 384 4
3328.2.bg \(\chi_{3328}(545, \cdot)\) n/a 432 4
3328.2.bi \(\chi_{3328}(31, \cdot)\) n/a 432 4
3328.2.bk \(\chi_{3328}(383, \cdot)\) n/a 432 4
3328.2.bn \(\chi_{3328}(63, \cdot)\) n/a 448 4
3328.2.bp \(\chi_{3328}(1089, \cdot)\) n/a 448 4
3328.2.br \(\chi_{3328}(321, \cdot)\) n/a 448 4
3328.2.bs \(\chi_{3328}(1727, \cdot)\) n/a 448 4
3328.2.bu \(\chi_{3328}(2047, \cdot)\) n/a 432 4
3328.2.bw \(\chi_{3328}(47, \cdot)\) n/a 880 8
3328.2.by \(\chi_{3328}(209, \cdot)\) n/a 768 8
3328.2.cb \(\chi_{3328}(337, \cdot)\) n/a 880 8
3328.2.cc \(\chi_{3328}(239, \cdot)\) n/a 880 8
3328.2.cf \(\chi_{3328}(479, \cdot)\) n/a 864 8
3328.2.ch \(\chi_{3328}(225, \cdot)\) n/a 864 8
3328.2.ci \(\chi_{3328}(289, \cdot)\) n/a 864 8
3328.2.ck \(\chi_{3328}(223, \cdot)\) n/a 864 8
3328.2.cn \(\chi_{3328}(135, \cdot)\) None 0 16
3328.2.cp \(\chi_{3328}(105, \cdot)\) None 0 16
3328.2.cr \(\chi_{3328}(25, \cdot)\) None 0 16
3328.2.cs \(\chi_{3328}(343, \cdot)\) None 0 16
3328.2.cv \(\chi_{3328}(175, \cdot)\) n/a 1760 16
3328.2.cx \(\chi_{3328}(81, \cdot)\) n/a 1760 16
3328.2.cy \(\chi_{3328}(17, \cdot)\) n/a 1760 16
3328.2.db \(\chi_{3328}(15, \cdot)\) n/a 1760 16
3328.2.dc \(\chi_{3328}(83, \cdot)\) n/a 14272 32
3328.2.de \(\chi_{3328}(77, \cdot)\) n/a 14272 32
3328.2.df \(\chi_{3328}(53, \cdot)\) n/a 12288 32
3328.2.di \(\chi_{3328}(99, \cdot)\) n/a 14272 32
3328.2.dk \(\chi_{3328}(71, \cdot)\) None 0 32
3328.2.dm \(\chi_{3328}(121, \cdot)\) None 0 32
3328.2.do \(\chi_{3328}(9, \cdot)\) None 0 32
3328.2.dr \(\chi_{3328}(7, \cdot)\) None 0 32
3328.2.dt \(\chi_{3328}(115, \cdot)\) n/a 28544 64
3328.2.dw \(\chi_{3328}(69, \cdot)\) n/a 28544 64
3328.2.dx \(\chi_{3328}(29, \cdot)\) n/a 28544 64
3328.2.dz \(\chi_{3328}(11, \cdot)\) n/a 28544 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3328))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3328)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(832))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1664))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3328))\)\(^{\oplus 1}\)