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Properties

Label 3440.2
Level 3440
Weight 2
Dimension 181646
Nonzero newspaces 56
Sturm bound 1419264
Trace bound 14

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Defining parameters

Level: \( N \) = \( 3440 = 2^{4} \cdot 5 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(1419264\)
Trace bound: \(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3440))\).

Total New Old
Modular forms 359520 183862 175658
Cusp forms 350113 181646 168467
Eisenstein series 9407 2216 7191

Trace form

\( 181646 q - 160 q^{2} - 122 q^{3} - 152 q^{4} - 299 q^{5} - 456 q^{6} - 114 q^{7} - 136 q^{8} - 34 q^{9} + O(q^{10}) \) \( 181646 q - 160 q^{2} - 122 q^{3} - 152 q^{4} - 299 q^{5} - 456 q^{6} - 114 q^{7} - 136 q^{8} - 34 q^{9} - 236 q^{10} - 346 q^{11} - 168 q^{12} - 190 q^{13} - 168 q^{14} - 145 q^{15} - 504 q^{16} - 342 q^{17} - 144 q^{18} - 70 q^{19} - 228 q^{20} - 542 q^{21} - 152 q^{22} - 90 q^{23} - 152 q^{24} - 43 q^{25} - 456 q^{26} - 134 q^{27} - 184 q^{28} - 170 q^{29} - 308 q^{30} - 434 q^{31} - 200 q^{32} - 410 q^{33} - 264 q^{34} - 209 q^{35} - 616 q^{36} - 246 q^{37} - 312 q^{38} - 166 q^{39} - 412 q^{40} - 182 q^{41} - 312 q^{42} - 116 q^{43} - 448 q^{44} - 351 q^{45} - 552 q^{46} - 50 q^{47} - 248 q^{48} - 346 q^{49} - 348 q^{50} - 306 q^{51} - 232 q^{52} - 198 q^{53} - 248 q^{54} - 149 q^{55} - 504 q^{56} + 38 q^{57} - 200 q^{58} - 70 q^{59} - 172 q^{60} - 630 q^{61} - 88 q^{62} - 178 q^{63} - 104 q^{64} - 467 q^{65} - 328 q^{66} - 226 q^{67} - 40 q^{68} - 234 q^{69} - 76 q^{70} - 466 q^{71} + 104 q^{72} + 2 q^{73} + 24 q^{74} - 401 q^{75} - 296 q^{76} - 194 q^{77} + 104 q^{78} - 302 q^{79} - 60 q^{80} - 1018 q^{81} - 24 q^{82} - 298 q^{83} + 120 q^{84} - 274 q^{85} - 424 q^{86} - 484 q^{87} + 56 q^{88} + 6 q^{89} - 4 q^{90} - 402 q^{91} - 168 q^{92} - 98 q^{93} - 104 q^{94} - 293 q^{95} - 408 q^{96} - 302 q^{97} - 240 q^{98} - 270 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3440))\)

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
3440.2.a \(\chi_{3440}(1, \cdot)\) 3440.2.a.a 1 1
3440.2.a.b 1
3440.2.a.c 1
3440.2.a.d 1
3440.2.a.e 1
3440.2.a.f 1
3440.2.a.g 2
3440.2.a.h 2
3440.2.a.i 2
3440.2.a.j 2
3440.2.a.k 3
3440.2.a.l 3
3440.2.a.m 3
3440.2.a.n 3
3440.2.a.o 3
3440.2.a.p 3
3440.2.a.q 4
3440.2.a.r 4
3440.2.a.s 4
3440.2.a.t 5
3440.2.a.u 5
3440.2.a.v 5
3440.2.a.w 5
3440.2.a.x 6
3440.2.a.y 7
3440.2.a.z 7
3440.2.b \(\chi_{3440}(3439, \cdot)\) n/a 132 1
3440.2.d \(\chi_{3440}(689, \cdot)\) n/a 126 1
3440.2.f \(\chi_{3440}(1721, \cdot)\) None 0 1
3440.2.h \(\chi_{3440}(1031, \cdot)\) None 0 1
3440.2.k \(\chi_{3440}(2409, \cdot)\) None 0 1
3440.2.m \(\chi_{3440}(1719, \cdot)\) None 0 1
3440.2.o \(\chi_{3440}(2751, \cdot)\) 3440.2.o.a 32 1
3440.2.o.b 56
3440.2.q \(\chi_{3440}(2401, \cdot)\) n/a 176 2
3440.2.t \(\chi_{3440}(603, \cdot)\) n/a 1008 2
3440.2.u \(\chi_{3440}(773, \cdot)\) n/a 1048 2
3440.2.x \(\chi_{3440}(861, \cdot)\) n/a 672 2
3440.2.y \(\chi_{3440}(171, \cdot)\) n/a 704 2
3440.2.z \(\chi_{3440}(1977, \cdot)\) None 0 2
3440.2.bc \(\chi_{3440}(1807, \cdot)\) n/a 252 2
3440.2.bd \(\chi_{3440}(87, \cdot)\) None 0 2
3440.2.bg \(\chi_{3440}(257, \cdot)\) n/a 260 2
3440.2.bh \(\chi_{3440}(859, \cdot)\) n/a 1048 2
3440.2.bi \(\chi_{3440}(1549, \cdot)\) n/a 1008 2
3440.2.bl \(\chi_{3440}(2323, \cdot)\) n/a 1008 2
3440.2.bm \(\chi_{3440}(2493, \cdot)\) n/a 1048 2
3440.2.bp \(\chi_{3440}(351, \cdot)\) n/a 176 2
3440.2.bs \(\chi_{3440}(1369, \cdot)\) None 0 2
3440.2.bu \(\chi_{3440}(2359, \cdot)\) None 0 2
3440.2.bx \(\chi_{3440}(681, \cdot)\) None 0 2
3440.2.bz \(\chi_{3440}(1671, \cdot)\) None 0 2
3440.2.cb \(\chi_{3440}(639, \cdot)\) n/a 264 2
3440.2.cd \(\chi_{3440}(49, \cdot)\) n/a 260 2
3440.2.ce \(\chi_{3440}(881, \cdot)\) n/a 528 6
3440.2.ch \(\chi_{3440}(37, \cdot)\) n/a 2096 4
3440.2.ci \(\chi_{3440}(1283, \cdot)\) n/a 2096 4
3440.2.cl \(\chi_{3440}(509, \cdot)\) n/a 2096 4
3440.2.cm \(\chi_{3440}(179, \cdot)\) n/a 2096 4
3440.2.co \(\chi_{3440}(767, \cdot)\) n/a 528 4
3440.2.cp \(\chi_{3440}(553, \cdot)\) None 0 4
3440.2.cs \(\chi_{3440}(897, \cdot)\) n/a 520 4
3440.2.ct \(\chi_{3440}(423, \cdot)\) None 0 4
3440.2.cv \(\chi_{3440}(811, \cdot)\) n/a 1408 4
3440.2.cw \(\chi_{3440}(221, \cdot)\) n/a 1408 4
3440.2.cz \(\chi_{3440}(1413, \cdot)\) n/a 2096 4
3440.2.da \(\chi_{3440}(307, \cdot)\) n/a 2096 4
3440.2.dd \(\chi_{3440}(39, \cdot)\) None 0 6
3440.2.df \(\chi_{3440}(489, \cdot)\) None 0 6
3440.2.di \(\chi_{3440}(591, \cdot)\) n/a 528 6
3440.2.dl \(\chi_{3440}(1569, \cdot)\) n/a 780 6
3440.2.dn \(\chi_{3440}(1279, \cdot)\) n/a 792 6
3440.2.dp \(\chi_{3440}(151, \cdot)\) None 0 6
3440.2.dr \(\chi_{3440}(41, \cdot)\) None 0 6
3440.2.ds \(\chi_{3440}(81, \cdot)\) n/a 1056 12
3440.2.dv \(\chi_{3440}(333, \cdot)\) n/a 6288 12
3440.2.dw \(\chi_{3440}(107, \cdot)\) n/a 6288 12
3440.2.dx \(\chi_{3440}(51, \cdot)\) n/a 4224 12
3440.2.dy \(\chi_{3440}(21, \cdot)\) n/a 4224 12
3440.2.eb \(\chi_{3440}(113, \cdot)\) n/a 1560 12
3440.2.ee \(\chi_{3440}(183, \cdot)\) None 0 12
3440.2.ef \(\chi_{3440}(47, \cdot)\) n/a 1584 12
3440.2.ei \(\chi_{3440}(137, \cdot)\) None 0 12
3440.2.el \(\chi_{3440}(269, \cdot)\) n/a 6288 12
3440.2.em \(\chi_{3440}(419, \cdot)\) n/a 6288 12
3440.2.en \(\chi_{3440}(237, \cdot)\) n/a 6288 12
3440.2.eo \(\chi_{3440}(1483, \cdot)\) n/a 6288 12
3440.2.er \(\chi_{3440}(71, \cdot)\) None 0 12
3440.2.et \(\chi_{3440}(281, \cdot)\) None 0 12
3440.2.ev \(\chi_{3440}(289, \cdot)\) n/a 1560 12
3440.2.ex \(\chi_{3440}(159, \cdot)\) n/a 1584 12
3440.2.fb \(\chi_{3440}(191, \cdot)\) n/a 1056 12
3440.2.fd \(\chi_{3440}(119, \cdot)\) None 0 12
3440.2.ff \(\chi_{3440}(9, \cdot)\) None 0 12
3440.2.fi \(\chi_{3440}(67, \cdot)\) n/a 12576 24
3440.2.fj \(\chi_{3440}(77, \cdot)\) n/a 12576 24
3440.2.fk \(\chi_{3440}(19, \cdot)\) n/a 12576 24
3440.2.fl \(\chi_{3440}(109, \cdot)\) n/a 12576 24
3440.2.fp \(\chi_{3440}(23, \cdot)\) None 0 24
3440.2.fq \(\chi_{3440}(33, \cdot)\) n/a 3120 24
3440.2.ft \(\chi_{3440}(73, \cdot)\) None 0 24
3440.2.fu \(\chi_{3440}(143, \cdot)\) n/a 3168 24
3440.2.fy \(\chi_{3440}(101, \cdot)\) n/a 8448 24
3440.2.fz \(\chi_{3440}(91, \cdot)\) n/a 8448 24
3440.2.ga \(\chi_{3440}(83, \cdot)\) n/a 12576 24
3440.2.gb \(\chi_{3440}(277, \cdot)\) n/a 12576 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3440))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3440)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(172))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(215))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(344))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(430))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(688))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(860))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1720))\)\(^{\oplus 2}\)