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Properties

Label 48.5
Level 48
Weight 5
Dimension 103
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 640
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(640\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(48))\).

Total New Old
Modular forms 284 113 171
Cusp forms 228 103 125
Eisenstein series 56 10 46

Trace form

\( 103 q - q^{3} + 8 q^{4} - 72 q^{5} - 68 q^{6} + 18 q^{7} + 180 q^{8} - 53 q^{9} + O(q^{10}) \) \( 103 q - q^{3} + 8 q^{4} - 72 q^{5} - 68 q^{6} + 18 q^{7} + 180 q^{8} - 53 q^{9} + 192 q^{10} - 192 q^{11} + 328 q^{12} - 542 q^{13} - 156 q^{14} + 252 q^{15} - 624 q^{16} + 360 q^{17} + 192 q^{18} + 1342 q^{19} - 1200 q^{20} + 526 q^{21} - 776 q^{22} - 2304 q^{23} + 364 q^{24} + 355 q^{25} + 2700 q^{26} + 1391 q^{27} + 3840 q^{28} + 792 q^{29} + 1644 q^{30} - 2518 q^{31} - 3360 q^{32} - 1652 q^{33} - 10360 q^{34} - 5184 q^{35} - 1712 q^{36} + 2722 q^{37} - 5880 q^{38} + 3730 q^{39} + 3336 q^{40} + 2664 q^{41} + 5260 q^{42} + 10270 q^{43} + 18840 q^{44} + 1716 q^{45} + 7584 q^{46} - 1952 q^{48} - 10155 q^{49} - 25884 q^{50} - 17920 q^{51} - 28272 q^{52} - 11496 q^{53} + 7060 q^{54} + 3072 q^{55} + 15456 q^{56} - 2210 q^{57} + 17096 q^{58} + 13056 q^{59} + 11640 q^{60} + 18114 q^{61} + 21852 q^{62} + 24882 q^{63} + 8192 q^{64} + 18288 q^{65} + 1948 q^{66} + 2174 q^{67} - 17280 q^{68} - 10980 q^{69} - 17256 q^{70} - 39936 q^{71} + 12612 q^{72} + 3830 q^{73} + 24204 q^{74} - 45357 q^{75} - 12976 q^{76} - 10752 q^{77} - 3832 q^{78} - 1174 q^{79} - 14232 q^{80} - 25689 q^{81} - 63496 q^{82} + 24000 q^{83} - 48008 q^{84} + 24176 q^{85} - 1200 q^{86} + 31488 q^{87} + 11328 q^{88} + 19080 q^{89} - 33864 q^{90} + 66756 q^{91} - 11664 q^{92} + 28778 q^{93} - 9720 q^{94} + 6920 q^{96} - 19442 q^{97} + 52968 q^{98} - 43652 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(48))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
48.5.b \(\chi_{48}(7, \cdot)\) None 0 1
48.5.e \(\chi_{48}(17, \cdot)\) 48.5.e.a 1 1
48.5.e.b 2
48.5.e.c 4
48.5.g \(\chi_{48}(31, \cdot)\) 48.5.g.a 2 1
48.5.g.b 2
48.5.h \(\chi_{48}(41, \cdot)\) None 0 1
48.5.i \(\chi_{48}(5, \cdot)\) 48.5.i.a 60 2
48.5.l \(\chi_{48}(19, \cdot)\) 48.5.l.a 32 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

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