Properties

 Label 2352.2 Level 2352 Weight 2 Dimension 60503 Nonzero newspaces 32 Sturm bound 602112 Trace bound 9

Defining parameters

 Level: $$N$$ = $$2352 = 2^{4} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$602112$$ Trace bound: $$9$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2352))$$.

Total New Old
Modular forms 153888 61375 92513
Cusp forms 147169 60503 86666
Eisenstein series 6719 872 5847

Trace form

 $$60503 q - 46 q^{3} - 128 q^{4} - 2 q^{5} - 68 q^{6} - 108 q^{7} - 12 q^{8} - 20 q^{9} + O(q^{10})$$ $$60503 q - 46 q^{3} - 128 q^{4} - 2 q^{5} - 68 q^{6} - 108 q^{7} - 12 q^{8} - 20 q^{9} - 128 q^{10} - 12 q^{11} - 60 q^{12} - 172 q^{13} - 91 q^{15} - 104 q^{16} + 2 q^{17} - 52 q^{18} - 130 q^{19} + 16 q^{20} - 102 q^{21} - 200 q^{22} - 64 q^{23} - 32 q^{24} - 117 q^{25} + 20 q^{26} - 40 q^{27} - 144 q^{28} - 58 q^{29} - 40 q^{30} - 170 q^{31} - 191 q^{33} - 128 q^{34} - 36 q^{35} - 92 q^{36} - 232 q^{37} - 8 q^{38} - 21 q^{39} - 144 q^{40} - 6 q^{41} - 138 q^{43} + 152 q^{44} + 7 q^{45} + 72 q^{46} + 72 q^{47} + 116 q^{48} - 228 q^{49} + 300 q^{50} + 49 q^{51} + 280 q^{52} + 206 q^{53} + 228 q^{54} + 98 q^{55} + 168 q^{56} + 157 q^{57} + 232 q^{58} + 124 q^{59} + 284 q^{60} + 96 q^{61} + 420 q^{62} - 24 q^{63} + 184 q^{64} + 180 q^{65} + 232 q^{66} - 2 q^{67} + 272 q^{68} + 91 q^{69} - 48 q^{70} + 16 q^{71} + 168 q^{72} + 52 q^{74} + 74 q^{75} - 56 q^{76} - 60 q^{78} - 106 q^{79} + 8 q^{80} - 32 q^{81} - 96 q^{82} - 36 q^{83} - 72 q^{84} - 258 q^{85} - 16 q^{86} + 27 q^{87} - 152 q^{88} - 6 q^{89} - 84 q^{90} + 102 q^{91} - 64 q^{92} + 29 q^{93} - 448 q^{94} + 304 q^{95} - 356 q^{96} - 274 q^{97} - 168 q^{98} - 16 q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2352))$$

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
2352.2.a $$\chi_{2352}(1, \cdot)$$ 2352.2.a.a 1 1
2352.2.a.b 1
2352.2.a.c 1
2352.2.a.d 1
2352.2.a.e 1
2352.2.a.f 1
2352.2.a.g 1
2352.2.a.h 1
2352.2.a.i 1
2352.2.a.j 1
2352.2.a.k 1
2352.2.a.l 1
2352.2.a.m 1
2352.2.a.n 1
2352.2.a.o 1
2352.2.a.p 1
2352.2.a.q 1
2352.2.a.r 1
2352.2.a.s 1
2352.2.a.t 1
2352.2.a.u 1
2352.2.a.v 1
2352.2.a.w 1
2352.2.a.x 1
2352.2.a.y 1
2352.2.a.z 2
2352.2.a.ba 2
2352.2.a.bb 2
2352.2.a.bc 2
2352.2.a.bd 2
2352.2.a.be 2
2352.2.a.bf 2
2352.2.a.bg 2
2352.2.b $$\chi_{2352}(1567, \cdot)$$ 2352.2.b.a 2 1
2352.2.b.b 2
2352.2.b.c 2
2352.2.b.d 2
2352.2.b.e 2
2352.2.b.f 2
2352.2.b.g 2
2352.2.b.h 2
2352.2.b.i 4
2352.2.b.j 4
2352.2.b.k 8
2352.2.b.l 8
2352.2.c $$\chi_{2352}(1177, \cdot)$$ None 0 1
2352.2.h $$\chi_{2352}(2255, \cdot)$$ 2352.2.h.a 2 1
2352.2.h.b 2
2352.2.h.c 2
2352.2.h.d 2
2352.2.h.e 2
2352.2.h.f 4
2352.2.h.g 4
2352.2.h.h 4
2352.2.h.i 4
2352.2.h.j 4
2352.2.h.k 4
2352.2.h.l 8
2352.2.h.m 8
2352.2.h.n 8
2352.2.h.o 8
2352.2.h.p 16
2352.2.i $$\chi_{2352}(2057, \cdot)$$ None 0 1
2352.2.j $$\chi_{2352}(1079, \cdot)$$ None 0 1
2352.2.k $$\chi_{2352}(881, \cdot)$$ 2352.2.k.a 2 1
2352.2.k.b 2
2352.2.k.c 2
2352.2.k.d 2
2352.2.k.e 4
2352.2.k.f 8
2352.2.k.g 8
2352.2.k.h 8
2352.2.k.i 16
2352.2.k.j 24
2352.2.p $$\chi_{2352}(391, \cdot)$$ None 0 1
2352.2.q $$\chi_{2352}(961, \cdot)$$ 2352.2.q.a 2 2
2352.2.q.b 2
2352.2.q.c 2
2352.2.q.d 2
2352.2.q.e 2
2352.2.q.f 2
2352.2.q.g 2
2352.2.q.h 2
2352.2.q.i 2
2352.2.q.j 2
2352.2.q.k 2
2352.2.q.l 2
2352.2.q.m 2
2352.2.q.n 2
2352.2.q.o 2
2352.2.q.p 2
2352.2.q.q 2
2352.2.q.r 2
2352.2.q.s 2
2352.2.q.t 2
2352.2.q.u 2
2352.2.q.v 2
2352.2.q.w 2
2352.2.q.x 2
2352.2.q.y 2
2352.2.q.z 2
2352.2.q.ba 4
2352.2.q.bb 4
2352.2.q.bc 4
2352.2.q.bd 4
2352.2.q.be 4
2352.2.q.bf 4
2352.2.q.bg 4
2352.2.s $$\chi_{2352}(491, \cdot)$$ n/a 636 2
2352.2.u $$\chi_{2352}(979, \cdot)$$ n/a 320 2
2352.2.w $$\chi_{2352}(589, \cdot)$$ n/a 328 2
2352.2.y $$\chi_{2352}(293, \cdot)$$ n/a 624 2
2352.2.bb $$\chi_{2352}(1207, \cdot)$$ None 0 2
2352.2.bc $$\chi_{2352}(1697, \cdot)$$ n/a 152 2
2352.2.bd $$\chi_{2352}(263, \cdot)$$ None 0 2
2352.2.bi $$\chi_{2352}(521, \cdot)$$ None 0 2
2352.2.bj $$\chi_{2352}(863, \cdot)$$ n/a 160 2
2352.2.bk $$\chi_{2352}(361, \cdot)$$ None 0 2
2352.2.bl $$\chi_{2352}(31, \cdot)$$ 2352.2.bl.a 2 2
2352.2.bl.b 2
2352.2.bl.c 2
2352.2.bl.d 2
2352.2.bl.e 2
2352.2.bl.f 2
2352.2.bl.g 2
2352.2.bl.h 2
2352.2.bl.i 2
2352.2.bl.j 2
2352.2.bl.k 2
2352.2.bl.l 2
2352.2.bl.m 4
2352.2.bl.n 4
2352.2.bl.o 8
2352.2.bl.p 8
2352.2.bl.q 8
2352.2.bl.r 8
2352.2.bl.s 8
2352.2.bl.t 8
2352.2.bo $$\chi_{2352}(337, \cdot)$$ n/a 336 6
2352.2.bp $$\chi_{2352}(509, \cdot)$$ n/a 1248 4
2352.2.br $$\chi_{2352}(373, \cdot)$$ n/a 640 4
2352.2.bt $$\chi_{2352}(19, \cdot)$$ n/a 640 4
2352.2.bv $$\chi_{2352}(275, \cdot)$$ n/a 1248 4
2352.2.bx $$\chi_{2352}(55, \cdot)$$ None 0 6
2352.2.cc $$\chi_{2352}(209, \cdot)$$ n/a 660 6
2352.2.cd $$\chi_{2352}(71, \cdot)$$ None 0 6
2352.2.ce $$\chi_{2352}(41, \cdot)$$ None 0 6
2352.2.cf $$\chi_{2352}(239, \cdot)$$ n/a 672 6
2352.2.ck $$\chi_{2352}(169, \cdot)$$ None 0 6
2352.2.cl $$\chi_{2352}(223, \cdot)$$ n/a 336 6
2352.2.cm $$\chi_{2352}(193, \cdot)$$ n/a 672 12
2352.2.cn $$\chi_{2352}(125, \cdot)$$ n/a 5328 12
2352.2.cp $$\chi_{2352}(85, \cdot)$$ n/a 2688 12
2352.2.cr $$\chi_{2352}(139, \cdot)$$ n/a 2688 12
2352.2.ct $$\chi_{2352}(155, \cdot)$$ n/a 5328 12
2352.2.cx $$\chi_{2352}(271, \cdot)$$ n/a 672 12
2352.2.cy $$\chi_{2352}(25, \cdot)$$ None 0 12
2352.2.cz $$\chi_{2352}(95, \cdot)$$ n/a 1344 12
2352.2.da $$\chi_{2352}(89, \cdot)$$ None 0 12
2352.2.df $$\chi_{2352}(23, \cdot)$$ None 0 12
2352.2.dg $$\chi_{2352}(17, \cdot)$$ n/a 1320 12
2352.2.dh $$\chi_{2352}(103, \cdot)$$ None 0 12
2352.2.dl $$\chi_{2352}(11, \cdot)$$ n/a 10656 24
2352.2.dn $$\chi_{2352}(115, \cdot)$$ n/a 5376 24
2352.2.dp $$\chi_{2352}(37, \cdot)$$ n/a 5376 24
2352.2.dr $$\chi_{2352}(5, \cdot)$$ n/a 10656 24

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2352))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2352)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(336))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(588))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(784))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1176))$$$$^{\oplus 2}$$