# Properties

 Label 2352.3 Level 2352 Weight 3 Dimension 121441 Nonzero newspaces 32 Sturm bound 903168 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$2352 = 2^{4} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$32$$ Sturm bound: $$903168$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(2352))$$.

Total New Old
Modular forms 304416 122315 182101
Cusp forms 297696 121441 176255
Eisenstein series 6720 874 5846

## Trace form

 $$121441 q - 46 q^{3} - 112 q^{4} + 12 q^{5} - 56 q^{6} - 108 q^{7} - 12 q^{8} - 26 q^{9} + O(q^{10})$$ $$121441 q - 46 q^{3} - 112 q^{4} + 12 q^{5} - 56 q^{6} - 108 q^{7} - 12 q^{8} - 26 q^{9} - 200 q^{10} + 32 q^{11} - 116 q^{12} - 172 q^{13} - 117 q^{15} - 104 q^{16} - 12 q^{17} - 108 q^{18} + 4 q^{19} + 80 q^{20} - 18 q^{21} - 144 q^{22} + 160 q^{23} - 80 q^{24} + 195 q^{25} - 100 q^{26} - 28 q^{27} - 144 q^{28} - 4 q^{29} + 96 q^{30} - 392 q^{31} + 160 q^{32} - 323 q^{33} + 112 q^{34} - 288 q^{35} + 100 q^{36} - 664 q^{37} + 168 q^{38} - 329 q^{39} + 16 q^{40} - 108 q^{41} - 504 q^{42} - 500 q^{43} - 2024 q^{44} - 1059 q^{45} - 2344 q^{46} - 576 q^{47} - 1772 q^{48} - 900 q^{49} - 1916 q^{50} - 157 q^{51} - 1784 q^{52} - 580 q^{53} - 560 q^{54} - 342 q^{55} + 168 q^{56} + 307 q^{57} + 464 q^{58} + 256 q^{59} + 972 q^{60} + 696 q^{61} + 2748 q^{62} + 186 q^{63} + 2168 q^{64} + 1720 q^{65} + 2080 q^{66} + 1092 q^{67} + 2672 q^{68} + 615 q^{69} + 1296 q^{70} + 896 q^{71} + 1224 q^{72} + 252 q^{73} + 348 q^{74} - 300 q^{75} + 728 q^{76} + 524 q^{78} + 280 q^{79} + 552 q^{80} - 342 q^{81} + 576 q^{82} - 160 q^{83} - 72 q^{84} + 10 q^{85} + 528 q^{86} + 345 q^{87} + 712 q^{88} + 228 q^{89} + 924 q^{90} - 1578 q^{91} + 1408 q^{92} + 407 q^{93} + 4752 q^{94} - 5760 q^{95} + 3548 q^{96} - 426 q^{97} + 2184 q^{98} - 692 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(2352))$$

We only show spaces with odd 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
2352.3.d $$\chi_{2352}(785, \cdot)$$ n/a 159 1
2352.3.e $$\chi_{2352}(1175, \cdot)$$ None 0 1
2352.3.f $$\chi_{2352}(97, \cdot)$$ 2352.3.f.a 2 1
2352.3.f.b 2
2352.3.f.c 2
2352.3.f.d 2
2352.3.f.e 4
2352.3.f.f 4
2352.3.f.g 8
2352.3.f.h 8
2352.3.f.i 8
2352.3.f.j 8
2352.3.f.k 8
2352.3.f.l 8
2352.3.f.m 16
2352.3.g $$\chi_{2352}(295, \cdot)$$ None 0 1
2352.3.l $$\chi_{2352}(1273, \cdot)$$ None 0 1
2352.3.m $$\chi_{2352}(1471, \cdot)$$ 2352.3.m.a 2 1
2352.3.m.b 2
2352.3.m.c 2
2352.3.m.d 4
2352.3.m.e 4
2352.3.m.f 4
2352.3.m.g 4
2352.3.m.h 4
2352.3.m.i 4
2352.3.m.j 4
2352.3.m.k 4
2352.3.m.l 4
2352.3.m.m 6
2352.3.m.n 6
2352.3.m.o 6
2352.3.m.p 6
2352.3.m.q 8
2352.3.m.r 8
2352.3.n $$\chi_{2352}(1961, \cdot)$$ None 0 1
2352.3.o $$\chi_{2352}(2351, \cdot)$$ n/a 160 1
2352.3.r $$\chi_{2352}(685, \cdot)$$ n/a 640 2
2352.3.t $$\chi_{2352}(197, \cdot)$$ n/a 1292 2
2352.3.v $$\chi_{2352}(587, \cdot)$$ n/a 1264 2
2352.3.x $$\chi_{2352}(883, \cdot)$$ n/a 656 2
2352.3.z $$\chi_{2352}(815, \cdot)$$ n/a 320 2
2352.3.ba $$\chi_{2352}(569, \cdot)$$ None 0 2
2352.3.be $$\chi_{2352}(79, \cdot)$$ n/a 160 2
2352.3.bf $$\chi_{2352}(313, \cdot)$$ None 0 2
2352.3.bg $$\chi_{2352}(1255, \cdot)$$ None 0 2
2352.3.bh $$\chi_{2352}(913, \cdot)$$ n/a 160 2
2352.3.bm $$\chi_{2352}(215, \cdot)$$ None 0 2
2352.3.bn $$\chi_{2352}(1745, \cdot)$$ n/a 312 2
2352.3.bq $$\chi_{2352}(67, \cdot)$$ n/a 1280 4
2352.3.bs $$\chi_{2352}(227, \cdot)$$ n/a 2528 4
2352.3.bu $$\chi_{2352}(557, \cdot)$$ n/a 2528 4
2352.3.bw $$\chi_{2352}(325, \cdot)$$ n/a 1280 4
2352.3.by $$\chi_{2352}(335, \cdot)$$ n/a 1344 6
2352.3.bz $$\chi_{2352}(281, \cdot)$$ None 0 6
2352.3.ca $$\chi_{2352}(127, \cdot)$$ n/a 672 6
2352.3.cb $$\chi_{2352}(265, \cdot)$$ None 0 6
2352.3.cg $$\chi_{2352}(631, \cdot)$$ None 0 6
2352.3.ch $$\chi_{2352}(433, \cdot)$$ n/a 672 6
2352.3.ci $$\chi_{2352}(167, \cdot)$$ None 0 6
2352.3.cj $$\chi_{2352}(113, \cdot)$$ n/a 1332 6
2352.3.co $$\chi_{2352}(43, \cdot)$$ n/a 5376 12
2352.3.cq $$\chi_{2352}(83, \cdot)$$ n/a 10704 12
2352.3.cs $$\chi_{2352}(29, \cdot)$$ n/a 10704 12
2352.3.cu $$\chi_{2352}(13, \cdot)$$ n/a 5376 12
2352.3.cv $$\chi_{2352}(65, \cdot)$$ n/a 2664 12
2352.3.cw $$\chi_{2352}(311, \cdot)$$ None 0 12
2352.3.db $$\chi_{2352}(145, \cdot)$$ n/a 1344 12
2352.3.dc $$\chi_{2352}(151, \cdot)$$ None 0 12
2352.3.dd $$\chi_{2352}(73, \cdot)$$ None 0 12
2352.3.de $$\chi_{2352}(319, \cdot)$$ n/a 1344 12
2352.3.di $$\chi_{2352}(137, \cdot)$$ None 0 12
2352.3.dj $$\chi_{2352}(47, \cdot)$$ n/a 2688 12
2352.3.dk $$\chi_{2352}(61, \cdot)$$ n/a 10752 24
2352.3.dm $$\chi_{2352}(53, \cdot)$$ n/a 21408 24
2352.3.do $$\chi_{2352}(59, \cdot)$$ n/a 21408 24
2352.3.dq $$\chi_{2352}(163, \cdot)$$ n/a 10752 24

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(2352))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(2352)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 20}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 16}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(336))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(588))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(784))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(1176))$$$$^{\oplus 2}$$