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Properties

Label 3240.2
Level 3240
Weight 2
Dimension 113376
Nonzero newspaces 36
Sturm bound 1119744
Trace bound 42

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Defining parameters

Level: \( N \) = \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(1119744\)
Trace bound: \(42\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3240))\).

Total New Old
Modular forms 285120 114720 170400
Cusp forms 274753 113376 161377
Eisenstein series 10367 1344 9023

Trace form

\( 113376 q - 48 q^{2} - 72 q^{3} - 80 q^{4} - 216 q^{6} - 80 q^{7} - 48 q^{8} - 144 q^{9} + O(q^{10}) \) \( 113376 q - 48 q^{2} - 72 q^{3} - 80 q^{4} - 216 q^{6} - 80 q^{7} - 48 q^{8} - 144 q^{9} - 174 q^{10} - 138 q^{11} - 72 q^{12} + 12 q^{13} - 48 q^{14} - 108 q^{15} - 240 q^{16} - 72 q^{17} - 72 q^{18} - 104 q^{19} - 72 q^{20} - 96 q^{22} - 24 q^{23} - 72 q^{24} - 234 q^{25} - 180 q^{26} - 72 q^{27} - 164 q^{28} - 36 q^{29} - 108 q^{30} - 276 q^{31} - 168 q^{32} - 144 q^{33} - 152 q^{34} - 114 q^{35} - 216 q^{36} - 36 q^{37} - 168 q^{38} - 72 q^{39} - 156 q^{40} - 366 q^{41} - 72 q^{42} - 158 q^{43} - 144 q^{44} - 54 q^{45} - 380 q^{46} - 264 q^{47} - 72 q^{48} - 244 q^{49} - 72 q^{50} - 342 q^{51} - 112 q^{52} - 180 q^{53} - 72 q^{54} - 266 q^{55} - 60 q^{56} - 252 q^{57} - 32 q^{58} - 330 q^{59} - 108 q^{60} - 120 q^{61} + 84 q^{62} - 180 q^{63} - 44 q^{64} - 270 q^{65} - 216 q^{66} - 218 q^{67} + 108 q^{68} - 36 q^{69} - 20 q^{70} - 300 q^{71} - 72 q^{72} - 280 q^{73} + 96 q^{74} - 108 q^{75} - 96 q^{76} - 120 q^{77} + 36 q^{78} - 212 q^{79} + 18 q^{80} - 432 q^{81} - 152 q^{82} - 228 q^{83} - 72 q^{84} - 72 q^{85} - 24 q^{86} - 72 q^{87} + 192 q^{88} - 96 q^{89} + 18 q^{90} - 308 q^{91} + 552 q^{92} + 108 q^{93} + 188 q^{94} + 78 q^{95} + 252 q^{96} - 70 q^{97} + 1092 q^{98} + 252 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3240))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3240.2.a \(\chi_{3240}(1, \cdot)\) 3240.2.a.a 1 1
3240.2.a.b 1
3240.2.a.c 1
3240.2.a.d 1
3240.2.a.e 1
3240.2.a.f 1
3240.2.a.g 2
3240.2.a.h 2
3240.2.a.i 2
3240.2.a.j 2
3240.2.a.k 2
3240.2.a.l 2
3240.2.a.m 2
3240.2.a.n 2
3240.2.a.o 2
3240.2.a.p 2
3240.2.a.q 3
3240.2.a.r 3
3240.2.a.s 4
3240.2.a.t 4
3240.2.a.u 4
3240.2.a.v 4
3240.2.b \(\chi_{3240}(971, \cdot)\) n/a 192 1
3240.2.d \(\chi_{3240}(2269, \cdot)\) n/a 280 1
3240.2.f \(\chi_{3240}(649, \cdot)\) 3240.2.f.a 2 1
3240.2.f.b 2
3240.2.f.c 2
3240.2.f.d 2
3240.2.f.e 2
3240.2.f.f 2
3240.2.f.g 6
3240.2.f.h 6
3240.2.f.i 16
3240.2.f.j 16
3240.2.f.k 16
3240.2.h \(\chi_{3240}(2591, \cdot)\) None 0 1
3240.2.k \(\chi_{3240}(1621, \cdot)\) n/a 192 1
3240.2.m \(\chi_{3240}(1619, \cdot)\) n/a 280 1
3240.2.o \(\chi_{3240}(3239, \cdot)\) None 0 1
3240.2.q \(\chi_{3240}(1081, \cdot)\) 3240.2.q.a 2 2
3240.2.q.b 2
3240.2.q.c 2
3240.2.q.d 2
3240.2.q.e 2
3240.2.q.f 2
3240.2.q.g 2
3240.2.q.h 2
3240.2.q.i 2
3240.2.q.j 2
3240.2.q.k 2
3240.2.q.l 2
3240.2.q.m 2
3240.2.q.n 2
3240.2.q.o 2
3240.2.q.p 2
3240.2.q.q 2
3240.2.q.r 2
3240.2.q.s 2
3240.2.q.t 2
3240.2.q.u 2
3240.2.q.v 2
3240.2.q.w 2
3240.2.q.x 2
3240.2.q.y 4
3240.2.q.z 4
3240.2.q.ba 4
3240.2.q.bb 4
3240.2.q.bc 4
3240.2.q.bd 4
3240.2.q.be 4
3240.2.q.bf 4
3240.2.q.bg 8
3240.2.q.bh 8
3240.2.s \(\chi_{3240}(1457, \cdot)\) n/a 144 2
3240.2.t \(\chi_{3240}(487, \cdot)\) None 0 2
3240.2.w \(\chi_{3240}(163, \cdot)\) n/a 560 2
3240.2.x \(\chi_{3240}(1133, \cdot)\) n/a 560 2
3240.2.bb \(\chi_{3240}(1079, \cdot)\) None 0 2
3240.2.bd \(\chi_{3240}(539, \cdot)\) n/a 568 2
3240.2.bf \(\chi_{3240}(541, \cdot)\) n/a 384 2
3240.2.bg \(\chi_{3240}(431, \cdot)\) None 0 2
3240.2.bi \(\chi_{3240}(1729, \cdot)\) n/a 144 2
3240.2.bk \(\chi_{3240}(109, \cdot)\) n/a 568 2
3240.2.bm \(\chi_{3240}(2051, \cdot)\) n/a 384 2
3240.2.bo \(\chi_{3240}(361, \cdot)\) n/a 216 6
3240.2.bp \(\chi_{3240}(1027, \cdot)\) n/a 1136 4
3240.2.bs \(\chi_{3240}(53, \cdot)\) n/a 1136 4
3240.2.bt \(\chi_{3240}(377, \cdot)\) n/a 288 4
3240.2.bw \(\chi_{3240}(703, \cdot)\) None 0 4
3240.2.bx \(\chi_{3240}(179, \cdot)\) n/a 1272 6
3240.2.cc \(\chi_{3240}(181, \cdot)\) n/a 864 6
3240.2.cd \(\chi_{3240}(359, \cdot)\) None 0 6
3240.2.cg \(\chi_{3240}(289, \cdot)\) n/a 324 6
3240.2.ch \(\chi_{3240}(251, \cdot)\) n/a 864 6
3240.2.ci \(\chi_{3240}(71, \cdot)\) None 0 6
3240.2.cj \(\chi_{3240}(469, \cdot)\) n/a 1272 6
3240.2.cm \(\chi_{3240}(121, \cdot)\) n/a 1944 18
3240.2.cp \(\chi_{3240}(197, \cdot)\) n/a 2544 12
3240.2.cq \(\chi_{3240}(127, \cdot)\) None 0 12
3240.2.ct \(\chi_{3240}(17, \cdot)\) n/a 648 12
3240.2.cu \(\chi_{3240}(307, \cdot)\) n/a 2544 12
3240.2.cx \(\chi_{3240}(229, \cdot)\) n/a 11592 18
3240.2.cy \(\chi_{3240}(119, \cdot)\) None 0 18
3240.2.da \(\chi_{3240}(11, \cdot)\) n/a 7776 18
3240.2.dc \(\chi_{3240}(191, \cdot)\) None 0 18
3240.2.de \(\chi_{3240}(59, \cdot)\) n/a 11592 18
3240.2.dh \(\chi_{3240}(49, \cdot)\) n/a 2916 18
3240.2.dj \(\chi_{3240}(61, \cdot)\) n/a 7776 18
3240.2.dk \(\chi_{3240}(77, \cdot)\) n/a 23184 36
3240.2.dn \(\chi_{3240}(43, \cdot)\) n/a 23184 36
3240.2.do \(\chi_{3240}(113, \cdot)\) n/a 5832 36
3240.2.dr \(\chi_{3240}(7, \cdot)\) None 0 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3240))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3240)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(810))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1080))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1620))\)\(^{\oplus 2}\)