Properties

Label 2940.2
Level 2940
Weight 2
Dimension 86314
Nonzero newspaces 48
Sturm bound 903168
Trace bound 9

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Defining parameters

Level: \( N \) = \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(903168\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2940))\).

Total New Old
Modular forms 230592 87474 143118
Cusp forms 220993 86314 134679
Eisenstein series 9599 1160 8439

Trace form

\( 86314 q + 6 q^{3} - 68 q^{4} + 14 q^{5} - 110 q^{6} + 16 q^{7} - 36 q^{8} - 90 q^{9} + O(q^{10}) \) \( 86314 q + 6 q^{3} - 68 q^{4} + 14 q^{5} - 110 q^{6} + 16 q^{7} - 36 q^{8} - 90 q^{9} - 146 q^{10} - 32 q^{11} - 94 q^{12} - 232 q^{13} - 48 q^{14} - 50 q^{15} - 276 q^{16} - 68 q^{17} - 74 q^{18} - 64 q^{19} + 20 q^{20} - 274 q^{21} - 4 q^{22} - 48 q^{23} + 30 q^{24} - 302 q^{25} + 136 q^{26} - 66 q^{27} + 24 q^{28} - 228 q^{29} + 57 q^{30} - 88 q^{31} + 140 q^{32} - 132 q^{33} + 132 q^{34} - 66 q^{35} - 18 q^{36} - 384 q^{37} + 88 q^{38} - 66 q^{39} - 14 q^{40} - 172 q^{41} + 66 q^{42} - 116 q^{43} + 96 q^{44} - 116 q^{45} - 84 q^{46} - 144 q^{47} + 220 q^{48} - 420 q^{49} + 8 q^{50} - 96 q^{51} + 212 q^{52} - 68 q^{53} + 118 q^{54} - 122 q^{55} + 132 q^{56} - 68 q^{57} + 292 q^{58} - 32 q^{59} + 161 q^{60} - 416 q^{61} + 376 q^{62} - 24 q^{63} + 292 q^{64} + 296 q^{65} + 74 q^{66} + 140 q^{67} + 368 q^{68} + 188 q^{69} + 186 q^{70} + 192 q^{71} + 18 q^{72} + 128 q^{73} + 264 q^{74} + 204 q^{75} + 116 q^{76} + 144 q^{77} + 10 q^{78} + 360 q^{79} + 418 q^{80} + 330 q^{81} + 584 q^{82} + 480 q^{83} + 300 q^{84} + 68 q^{85} + 580 q^{86} + 524 q^{87} + 896 q^{88} + 404 q^{89} + 180 q^{90} + 376 q^{91} + 308 q^{92} + 680 q^{93} + 728 q^{94} + 300 q^{95} + 436 q^{96} + 624 q^{97} + 1092 q^{98} + 320 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2940))\)

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
2940.2.a \(\chi_{2940}(1, \cdot)\) 2940.2.a.a 1 1
2940.2.a.b 1
2940.2.a.c 1
2940.2.a.d 1
2940.2.a.e 1
2940.2.a.f 1
2940.2.a.g 1
2940.2.a.h 1
2940.2.a.i 1
2940.2.a.j 1
2940.2.a.k 1
2940.2.a.l 1
2940.2.a.m 2
2940.2.a.n 2
2940.2.a.o 2
2940.2.a.p 2
2940.2.a.q 2
2940.2.a.r 2
2940.2.a.s 2
2940.2.a.t 2
2940.2.c \(\chi_{2940}(391, \cdot)\) n/a 160 1
2940.2.d \(\chi_{2940}(881, \cdot)\) 2940.2.d.a 10 1
2940.2.d.b 10
2940.2.d.c 16
2940.2.d.d 16
2940.2.f \(\chi_{2940}(1469, \cdot)\) 2940.2.f.a 32 1
2940.2.f.b 48
2940.2.i \(\chi_{2940}(979, \cdot)\) n/a 240 1
2940.2.k \(\chi_{2940}(589, \cdot)\) 2940.2.k.a 2 1
2940.2.k.b 2
2940.2.k.c 2
2940.2.k.d 2
2940.2.k.e 2
2940.2.k.f 8
2940.2.k.g 8
2940.2.k.h 16
2940.2.l \(\chi_{2940}(1079, \cdot)\) n/a 472 1
2940.2.n \(\chi_{2940}(491, \cdot)\) n/a 328 1
2940.2.q \(\chi_{2940}(361, \cdot)\) 2940.2.q.a 2 2
2940.2.q.b 2
2940.2.q.c 2
2940.2.q.d 2
2940.2.q.e 2
2940.2.q.f 2
2940.2.q.g 2
2940.2.q.h 2
2940.2.q.i 2
2940.2.q.j 2
2940.2.q.k 2
2940.2.q.l 2
2940.2.q.m 2
2940.2.q.n 2
2940.2.q.o 4
2940.2.q.p 4
2940.2.q.q 4
2940.2.q.r 4
2940.2.q.s 4
2940.2.q.t 4
2940.2.s \(\chi_{2940}(197, \cdot)\) n/a 164 2
2940.2.t \(\chi_{2940}(883, \cdot)\) n/a 492 2
2940.2.w \(\chi_{2940}(587, \cdot)\) n/a 928 2
2940.2.x \(\chi_{2940}(97, \cdot)\) 2940.2.x.a 24 2
2940.2.x.b 24
2940.2.x.c 32
2940.2.ba \(\chi_{2940}(1439, \cdot)\) n/a 928 2
2940.2.bb \(\chi_{2940}(949, \cdot)\) 2940.2.bb.a 4 2
2940.2.bb.b 4
2940.2.bb.c 4
2940.2.bb.d 4
2940.2.bb.e 4
2940.2.bb.f 4
2940.2.bb.g 4
2940.2.bb.h 4
2940.2.bb.i 16
2940.2.bb.j 32
2940.2.bf \(\chi_{2940}(851, \cdot)\) n/a 640 2
2940.2.bh \(\chi_{2940}(521, \cdot)\) n/a 108 2
2940.2.bi \(\chi_{2940}(31, \cdot)\) n/a 320 2
2940.2.bk \(\chi_{2940}(19, \cdot)\) n/a 480 2
2940.2.bn \(\chi_{2940}(509, \cdot)\) n/a 160 2
2940.2.bo \(\chi_{2940}(421, \cdot)\) n/a 216 6
2940.2.bp \(\chi_{2940}(313, \cdot)\) n/a 160 4
2940.2.bs \(\chi_{2940}(227, \cdot)\) n/a 1856 4
2940.2.bt \(\chi_{2940}(67, \cdot)\) n/a 960 4
2940.2.bw \(\chi_{2940}(557, \cdot)\) n/a 320 4
2940.2.by \(\chi_{2940}(71, \cdot)\) n/a 2688 6
2940.2.ca \(\chi_{2940}(239, \cdot)\) n/a 3984 6
2940.2.cd \(\chi_{2940}(169, \cdot)\) n/a 336 6
2940.2.cf \(\chi_{2940}(139, \cdot)\) n/a 2016 6
2940.2.cg \(\chi_{2940}(209, \cdot)\) n/a 672 6
2940.2.ci \(\chi_{2940}(41, \cdot)\) n/a 456 6
2940.2.cl \(\chi_{2940}(811, \cdot)\) n/a 1344 6
2940.2.cm \(\chi_{2940}(121, \cdot)\) n/a 456 12
2940.2.cn \(\chi_{2940}(83, \cdot)\) n/a 7968 12
2940.2.cq \(\chi_{2940}(13, \cdot)\) n/a 672 12
2940.2.cr \(\chi_{2940}(113, \cdot)\) n/a 1344 12
2940.2.cu \(\chi_{2940}(43, \cdot)\) n/a 4032 12
2940.2.cw \(\chi_{2940}(89, \cdot)\) n/a 1344 12
2940.2.cx \(\chi_{2940}(199, \cdot)\) n/a 4032 12
2940.2.cz \(\chi_{2940}(271, \cdot)\) n/a 2688 12
2940.2.dc \(\chi_{2940}(101, \cdot)\) n/a 888 12
2940.2.de \(\chi_{2940}(11, \cdot)\) n/a 5376 12
2940.2.dg \(\chi_{2940}(109, \cdot)\) n/a 672 12
2940.2.dj \(\chi_{2940}(179, \cdot)\) n/a 7968 12
2940.2.dl \(\chi_{2940}(163, \cdot)\) n/a 8064 24
2940.2.dm \(\chi_{2940}(53, \cdot)\) n/a 2688 24
2940.2.dp \(\chi_{2940}(73, \cdot)\) n/a 1344 24
2940.2.dq \(\chi_{2940}(47, \cdot)\) n/a 15936 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2940))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2940)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(980))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1470))\)\(^{\oplus 2}\)