# Properties

 Label 304.5 Level 304 Weight 5 Dimension 6367 Nonzero newspaces 12 Sturm bound 28800 Trace bound 7

## Defining parameters

 Level: $$N$$ = $$304 = 2^{4} \cdot 19$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$12$$ Sturm bound: $$28800$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(304))$$.

Total New Old
Modular forms 11772 6521 5251
Cusp forms 11268 6367 4901
Eisenstein series 504 154 350

## Trace form

 $$6367q - 32q^{2} - 23q^{3} - 20q^{4} - 113q^{5} - 164q^{6} - 19q^{7} + 148q^{8} + 435q^{9} + O(q^{10})$$ $$6367q - 32q^{2} - 23q^{3} - 20q^{4} - 113q^{5} - 164q^{6} - 19q^{7} + 148q^{8} + 435q^{9} + 164q^{10} - 215q^{11} + 628q^{12} - 753q^{13} - 124q^{14} - 27q^{15} + 300q^{16} + 431q^{17} - 2816q^{18} + 679q^{19} - 3872q^{20} - 1253q^{21} - 1836q^{22} - 2323q^{23} + 3708q^{24} + 1195q^{25} + 6796q^{26} + 3301q^{27} + 7532q^{28} + 3919q^{29} + 7444q^{30} - 27q^{31} - 6452q^{32} - 6985q^{33} - 15052q^{34} - 2707q^{35} - 22972q^{36} + 1496q^{37} - 3604q^{38} - 5422q^{39} + 10252q^{40} - 657q^{41} + 34092q^{42} - 3415q^{43} + 29236q^{44} + 5127q^{45} + 10596q^{46} - 27q^{47} - 13812q^{48} - 7977q^{49} - 40176q^{50} + 5997q^{51} - 40940q^{52} - 1457q^{53} - 21604q^{54} + 23533q^{55} + 13868q^{56} + 11127q^{57} + 40840q^{58} + 5545q^{59} + 59804q^{60} + 42303q^{61} + 22908q^{62} + 15525q^{63} - 31652q^{64} - 30457q^{65} - 60332q^{66} - 76503q^{67} - 36100q^{68} - 104837q^{69} - 30628q^{70} - 67171q^{71} + 35380q^{72} - 3937q^{73} + 47524q^{74} - 35176q^{75} + 23960q^{76} + 65150q^{77} + 16068q^{78} + 71541q^{79} - 2804q^{80} + 91583q^{81} - 32068q^{82} + 78601q^{83} - 39284q^{84} + 39531q^{85} + 9556q^{86} + 137421q^{87} - 14612q^{88} - 51057q^{89} + 10796q^{90} - 29203q^{91} + 29228q^{92} - 88829q^{93} - 900q^{94} - 27q^{95} - 12200q^{96} + 6319q^{97} + 24456q^{98} - 98455q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(304))$$

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
304.5.d $$\chi_{304}(191, \cdot)$$ 304.5.d.a 12 1
304.5.d.b 24
304.5.e $$\chi_{304}(113, \cdot)$$ 304.5.e.a 1 1
304.5.e.b 2
304.5.e.c 4
304.5.e.d 4
304.5.e.e 8
304.5.e.f 20
304.5.f $$\chi_{304}(39, \cdot)$$ None 0 1
304.5.g $$\chi_{304}(265, \cdot)$$ None 0 1
304.5.j $$\chi_{304}(37, \cdot)$$ n/a 316 2
304.5.l $$\chi_{304}(115, \cdot)$$ n/a 288 2
304.5.o $$\chi_{304}(7, \cdot)$$ None 0 2
304.5.p $$\chi_{304}(217, \cdot)$$ None 0 2
304.5.q $$\chi_{304}(159, \cdot)$$ 304.5.q.a 24 2
304.5.q.b 28
304.5.q.c 28
304.5.r $$\chi_{304}(65, \cdot)$$ 304.5.r.a 10 2
304.5.r.b 12
304.5.r.c 16
304.5.r.d 40
304.5.w $$\chi_{304}(69, \cdot)$$ n/a 632 4
304.5.y $$\chi_{304}(11, \cdot)$$ n/a 632 4
304.5.z $$\chi_{304}(33, \cdot)$$ n/a 234 6
304.5.ba $$\chi_{304}(41, \cdot)$$ None 0 6
304.5.bc $$\chi_{304}(23, \cdot)$$ None 0 6
304.5.bf $$\chi_{304}(47, \cdot)$$ n/a 240 6
304.5.bh $$\chi_{304}(35, \cdot)$$ n/a 1896 12
304.5.bj $$\chi_{304}(13, \cdot)$$ n/a 1896 12

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

## Decomposition of $$S_{5}^{\mathrm{old}}(\Gamma_1(304))$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(\Gamma_1(304)) \cong$$ $$S_{5}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 6}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 4}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 2}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 5}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 4}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 3}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 2}$$