# Properties

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

## 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

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