# Properties

 Label 48.11 Level 48 Weight 11 Dimension 265 Nonzero newspaces 4 Newform subspaces 10 Sturm bound 1408 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$48 = 2^{4} \cdot 3$$ Weight: $$k$$ = $$11$$ Nonzero newspaces: $$4$$ Newform subspaces: $$10$$ Sturm bound: $$1408$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{11}(\Gamma_1(48))$$.

Total New Old
Modular forms 668 275 393
Cusp forms 612 265 347
Eisenstein series 56 10 46

## Trace form

 $$265 q - q^{3} + 2504 q^{4} - 9348 q^{5} + 17212 q^{6} + 14634 q^{7} - 138252 q^{8} - 186227 q^{9} + O(q^{10})$$ $$265 q - q^{3} + 2504 q^{4} - 9348 q^{5} + 17212 q^{6} + 14634 q^{7} - 138252 q^{8} - 186227 q^{9} + 294720 q^{10} + 91808 q^{11} + 10984 q^{12} + 576430 q^{13} - 1519772 q^{14} + 979164 q^{15} + 5020176 q^{16} - 1358652 q^{17} - 968352 q^{18} + 15084574 q^{19} - 4750000 q^{20} - 6450170 q^{21} + 17898424 q^{22} + 16559488 q^{23} - 13901972 q^{24} - 21959447 q^{25} + 48999500 q^{26} + 28486391 q^{27} - 13731840 q^{28} + 21408908 q^{29} - 35180724 q^{30} - 9985102 q^{31} + 149295520 q^{32} - 79408508 q^{33} - 182251768 q^{34} - 68411424 q^{35} - 301603376 q^{36} + 332704558 q^{37} + 186228168 q^{38} - 48282422 q^{39} - 2195064 q^{40} - 517450140 q^{41} - 745874420 q^{42} - 493184498 q^{43} + 704131288 q^{44} + 314356056 q^{45} + 1530741600 q^{46} - 1892858912 q^{48} - 4247387457 q^{49} - 232399196 q^{50} + 591820928 q^{51} + 2241232080 q^{52} - 288413332 q^{53} + 2522322292 q^{54} + 1388659008 q^{55} + 1023251488 q^{56} - 806110322 q^{57} - 167096824 q^{58} - 1499085440 q^{59} - 3393534408 q^{60} - 1370014626 q^{61} + 2988847452 q^{62} + 1329318330 q^{63} + 12300261248 q^{64} - 6306719720 q^{65} - 899839364 q^{66} + 11379079742 q^{67} - 7306925248 q^{68} - 2328604596 q^{69} - 668299752 q^{70} - 15145776640 q^{71} + 6208690692 q^{72} + 840603914 q^{73} + 9400896780 q^{74} + 12051058539 q^{75} + 11231771024 q^{76} + 6349812224 q^{77} - 23601460696 q^{78} - 11725035694 q^{79} - 6032827608 q^{80} - 26541826743 q^{81} + 26775504824 q^{82} - 14192131360 q^{83} + 34970588728 q^{84} + 25400002040 q^{85} - 20085853872 q^{86} - 5040791904 q^{87} - 57389532096 q^{88} + 8742105588 q^{89} + 31475173944 q^{90} - 17590914204 q^{91} - 3251386640 q^{92} - 16175751502 q^{93} + 47607497736 q^{94} - 51213597688 q^{96} + 10140534706 q^{97} + 22401405928 q^{98} - 40080071684 q^{99} + O(q^{100})$$

## Decomposition of $$S_{11}^{\mathrm{new}}(\Gamma_1(48))$$

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
48.11.b $$\chi_{48}(7, \cdot)$$ None 0 1
48.11.e $$\chi_{48}(17, \cdot)$$ 48.11.e.a 1 1
48.11.e.b 2
48.11.e.c 2
48.11.e.d 4
48.11.e.e 10
48.11.g $$\chi_{48}(31, \cdot)$$ 48.11.g.a 2 1
48.11.g.b 4
48.11.g.c 4
48.11.h $$\chi_{48}(41, \cdot)$$ None 0 1
48.11.i $$\chi_{48}(5, \cdot)$$ 48.11.i.a 156 2
48.11.l $$\chi_{48}(19, \cdot)$$ 48.11.l.a 80 2

## Decomposition of $$S_{11}^{\mathrm{old}}(\Gamma_1(48))$$ into lower level spaces

$$S_{11}^{\mathrm{old}}(\Gamma_1(48)) \cong$$ $$S_{11}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 5}$$$$\oplus$$$$S_{11}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 6}$$$$\oplus$$$$S_{11}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 4}$$$$\oplus$$$$S_{11}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 4}$$$$\oplus$$$$S_{11}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 3}$$$$\oplus$$$$S_{11}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 2}$$$$\oplus$$$$S_{11}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 2}$$