# Properties

 Label 832.4 Level 832 Weight 4 Dimension 35614 Nonzero newspaces 28 Sturm bound 172032 Trace bound 17

## Defining parameters

 Level: $$N$$ = $$832 = 2^{6} \cdot 13$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$28$$ Sturm bound: $$172032$$ Trace bound: $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(832))$$.

Total New Old
Modular forms 65376 36098 29278
Cusp forms 63648 35614 28034
Eisenstein series 1728 484 1244

## Trace form

 $$35614 q - 80 q^{2} - 60 q^{3} - 80 q^{4} - 80 q^{5} - 80 q^{6} - 56 q^{7} - 80 q^{8} - 46 q^{9} + O(q^{10})$$ $$35614 q - 80 q^{2} - 60 q^{3} - 80 q^{4} - 80 q^{5} - 80 q^{6} - 56 q^{7} - 80 q^{8} - 46 q^{9} - 80 q^{10} - 20 q^{11} - 80 q^{12} - 160 q^{13} - 176 q^{14} - 304 q^{15} - 80 q^{16} - 348 q^{17} - 80 q^{18} - 108 q^{19} - 80 q^{20} - 56 q^{21} - 1024 q^{22} - 56 q^{23} - 2080 q^{24} - 202 q^{25} - 48 q^{26} + 240 q^{27} + 1440 q^{28} + 720 q^{29} + 4560 q^{30} + 664 q^{31} + 2400 q^{32} + 1904 q^{33} + 1920 q^{34} + 896 q^{35} + 1680 q^{36} + 960 q^{37} - 960 q^{38} - 64 q^{39} - 3456 q^{40} - 2148 q^{41} - 6400 q^{42} - 1732 q^{43} - 2080 q^{44} - 3048 q^{45} - 80 q^{46} - 1944 q^{47} - 80 q^{48} - 2266 q^{49} + 5632 q^{50} - 9008 q^{51} + 3224 q^{52} - 992 q^{53} + 3376 q^{54} - 1208 q^{55} - 864 q^{56} + 2056 q^{57} - 4832 q^{58} + 8860 q^{59} - 9872 q^{60} + 2080 q^{61} - 6064 q^{62} + 15296 q^{63} - 12176 q^{64} + 2032 q^{65} - 11248 q^{66} + 11988 q^{67} - 4208 q^{68} + 1192 q^{69} - 4112 q^{70} + 840 q^{71} + 1216 q^{72} - 2148 q^{73} + 5184 q^{74} - 14796 q^{75} + 11824 q^{76} - 6328 q^{77} + 1904 q^{78} - 20288 q^{79} - 8608 q^{80} - 13778 q^{81} - 14000 q^{82} - 5180 q^{83} - 8368 q^{84} - 3392 q^{85} + 960 q^{86} - 56 q^{87} + 6160 q^{88} + 7036 q^{89} + 18640 q^{90} + 3268 q^{91} + 25056 q^{92} + 16672 q^{93} + 17776 q^{94} + 13728 q^{95} + 25760 q^{96} + 18644 q^{97} + 24128 q^{98} + 9428 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(832))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
832.4.a $$\chi_{832}(1, \cdot)$$ 832.4.a.a 1 1
832.4.a.b 1
832.4.a.c 1
832.4.a.d 1
832.4.a.e 1
832.4.a.f 1
832.4.a.g 1
832.4.a.h 1
832.4.a.i 1
832.4.a.j 1
832.4.a.k 1
832.4.a.l 1
832.4.a.m 1
832.4.a.n 1
832.4.a.o 1
832.4.a.p 1
832.4.a.q 1
832.4.a.r 1
832.4.a.s 2
832.4.a.t 2
832.4.a.u 2
832.4.a.v 2
832.4.a.w 2
832.4.a.x 2
832.4.a.y 2
832.4.a.z 2
832.4.a.ba 3
832.4.a.bb 3
832.4.a.bc 3
832.4.a.bd 3
832.4.a.be 4
832.4.a.bf 5
832.4.a.bg 5
832.4.a.bh 6
832.4.a.bi 6
832.4.b $$\chi_{832}(417, \cdot)$$ 832.4.b.a 12 1
832.4.b.b 12
832.4.b.c 24
832.4.b.d 24
832.4.e $$\chi_{832}(545, \cdot)$$ 832.4.e.a 4 1
832.4.e.b 8
832.4.e.c 8
832.4.e.d 8
832.4.e.e 56
832.4.f $$\chi_{832}(129, \cdot)$$ 832.4.f.a 2 1
832.4.f.b 2
832.4.f.c 2
832.4.f.d 2
832.4.f.e 2
832.4.f.f 2
832.4.f.g 2
832.4.f.h 4
832.4.f.i 4
832.4.f.j 4
832.4.f.k 10
832.4.f.l 10
832.4.f.m 16
832.4.f.n 20
832.4.i $$\chi_{832}(321, \cdot)$$ n/a 164 2
832.4.k $$\chi_{832}(255, \cdot)$$ n/a 164 2
832.4.l $$\chi_{832}(239, \cdot)$$ n/a 164 2
832.4.n $$\chi_{832}(209, \cdot)$$ n/a 144 2
832.4.p $$\chi_{832}(337, \cdot)$$ n/a 164 2
832.4.s $$\chi_{832}(47, \cdot)$$ n/a 164 2
832.4.u $$\chi_{832}(31, \cdot)$$ n/a 168 2
832.4.w $$\chi_{832}(257, \cdot)$$ n/a 164 2
832.4.z $$\chi_{832}(289, \cdot)$$ n/a 168 2
832.4.ba $$\chi_{832}(225, \cdot)$$ n/a 168 2
832.4.bd $$\chi_{832}(343, \cdot)$$ None 0 4
832.4.bf $$\chi_{832}(105, \cdot)$$ None 0 4
832.4.bg $$\chi_{832}(25, \cdot)$$ None 0 4
832.4.bi $$\chi_{832}(135, \cdot)$$ None 0 4
832.4.bk $$\chi_{832}(223, \cdot)$$ n/a 336 4
832.4.bn $$\chi_{832}(175, \cdot)$$ n/a 328 4
832.4.bp $$\chi_{832}(17, \cdot)$$ n/a 328 4
832.4.br $$\chi_{832}(81, \cdot)$$ n/a 328 4
832.4.bs $$\chi_{832}(15, \cdot)$$ n/a 328 4
832.4.bu $$\chi_{832}(63, \cdot)$$ n/a 328 4
832.4.bw $$\chi_{832}(99, \cdot)$$ n/a 2672 8
832.4.by $$\chi_{832}(53, \cdot)$$ n/a 2304 8
832.4.cb $$\chi_{832}(77, \cdot)$$ n/a 2672 8
832.4.cc $$\chi_{832}(83, \cdot)$$ n/a 2672 8
832.4.cf $$\chi_{832}(71, \cdot)$$ None 0 8
832.4.ch $$\chi_{832}(121, \cdot)$$ None 0 8
832.4.ci $$\chi_{832}(9, \cdot)$$ None 0 8
832.4.ck $$\chi_{832}(7, \cdot)$$ None 0 8
832.4.cn $$\chi_{832}(11, \cdot)$$ n/a 5344 16
832.4.cp $$\chi_{832}(29, \cdot)$$ n/a 5344 16
832.4.cq $$\chi_{832}(69, \cdot)$$ n/a 5344 16
832.4.ct $$\chi_{832}(115, \cdot)$$ n/a 5344 16

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(832))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(832)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 14}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 7}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(416))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(832))$$$$^{\oplus 1}$$