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Properties

Label 48.8
Level 48
Weight 8
Dimension 185
Nonzero newspaces 4
Newform subspaces 12
Sturm bound 1024
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 12 \)
Sturm bound: \(1024\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(48))\).

Total New Old
Modular forms 476 193 283
Cusp forms 420 185 235
Eisenstein series 56 8 48

Trace form

\( 185 q - 29 q^{3} + 360 q^{4} - 278 q^{5} + 172 q^{6} - 328 q^{7} + 2004 q^{8} + 1749 q^{9} + O(q^{10}) \) \( 185 q - 29 q^{3} + 360 q^{4} - 278 q^{5} + 172 q^{6} - 328 q^{7} + 2004 q^{8} + 1749 q^{9} - 25952 q^{10} - 3612 q^{11} + 27352 q^{12} + 3018 q^{13} - 44028 q^{14} + 33750 q^{15} - 52784 q^{16} + 1454 q^{17} + 41584 q^{18} - 183040 q^{19} + 82000 q^{20} - 7892 q^{21} - 99784 q^{22} + 230984 q^{23} - 276372 q^{24} - 121801 q^{25} + 363980 q^{26} + 218359 q^{27} + 129920 q^{28} - 8734 q^{29} - 165380 q^{30} - 348464 q^{31} - 571200 q^{32} - 249376 q^{33} - 1188984 q^{34} + 82680 q^{35} + 829712 q^{36} - 194574 q^{37} + 1921576 q^{38} + 347906 q^{39} + 840776 q^{40} + 33702 q^{41} - 3120084 q^{42} - 646352 q^{43} + 1417400 q^{44} + 601854 q^{45} - 1954496 q^{46} + 97920 q^{47} + 903072 q^{48} + 2951533 q^{49} + 2069988 q^{50} - 422646 q^{51} - 4600400 q^{52} - 3045958 q^{53} + 282548 q^{54} + 1936608 q^{55} + 9766848 q^{56} + 4241544 q^{57} + 3314376 q^{58} + 3139756 q^{59} - 5474344 q^{60} - 8654870 q^{61} - 14719044 q^{62} - 2233656 q^{63} + 76992 q^{64} + 463788 q^{65} - 421076 q^{66} + 20314336 q^{67} + 9981536 q^{68} + 6422812 q^{69} + 14142488 q^{70} - 9291464 q^{71} - 823388 q^{72} + 3579010 q^{73} + 18583468 q^{74} - 6654319 q^{75} - 15895824 q^{76} - 19878608 q^{77} - 31906248 q^{78} + 18725040 q^{79} - 26364088 q^{80} - 18019975 q^{81} - 13930664 q^{82} + 3459852 q^{83} - 5064872 q^{84} - 7384508 q^{85} + 32307920 q^{86} - 38674854 q^{87} + 96492352 q^{88} + 17795334 q^{89} + 28364600 q^{90} + 199424 q^{91} - 16335952 q^{92} - 24594728 q^{93} - 117047480 q^{94} + 59742664 q^{95} - 60505976 q^{96} - 46238590 q^{97} - 8969560 q^{98} - 7334224 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.8.a \(\chi_{48}(1, \cdot)\) 48.8.a.a 1 1
48.8.a.b 1
48.8.a.c 1
48.8.a.d 1
48.8.a.e 1
48.8.a.f 1
48.8.a.g 1
48.8.c \(\chi_{48}(47, \cdot)\) 48.8.c.a 2 1
48.8.c.b 4
48.8.c.c 8
48.8.d \(\chi_{48}(25, \cdot)\) None 0 1
48.8.f \(\chi_{48}(23, \cdot)\) None 0 1
48.8.j \(\chi_{48}(13, \cdot)\) 48.8.j.a 56 2
48.8.k \(\chi_{48}(11, \cdot)\) 48.8.k.a 108 2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

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