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Properties

Label 48.6
Level 48
Weight 6
Dimension 131
Nonzero newspaces 4
Newform subspaces 11
Sturm bound 768
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 11 \)
Sturm bound: \(768\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(48))\).

Total New Old
Modular forms 348 139 209
Cusp forms 292 131 161
Eisenstein series 56 8 48

Trace form

\( 131 q + 7 q^{3} + 40 q^{4} + 38 q^{5} - 116 q^{6} - 168 q^{7} - 492 q^{8} + 471 q^{9} + O(q^{10}) \) \( 131 q + 7 q^{3} + 40 q^{4} + 38 q^{5} - 116 q^{6} - 168 q^{7} - 492 q^{8} + 471 q^{9} + 864 q^{10} + 1812 q^{11} - 8 q^{12} - 242 q^{13} + 324 q^{14} - 2250 q^{15} + 4176 q^{16} + 202 q^{17} - 4400 q^{18} + 9680 q^{19} - 7600 q^{20} + 1972 q^{21} + 1208 q^{22} - 4664 q^{23} + 7788 q^{24} - 1955 q^{25} - 12980 q^{26} - 3005 q^{27} - 1920 q^{28} - 8354 q^{29} - 740 q^{30} + 20336 q^{31} + 44160 q^{32} + 7592 q^{33} + 31112 q^{34} - 19176 q^{35} - 32368 q^{36} - 12746 q^{37} - 72088 q^{38} - 40174 q^{39} - 90424 q^{40} - 10878 q^{41} - 2964 q^{42} + 22176 q^{43} + 43768 q^{44} + 32538 q^{45} + 121984 q^{46} + 35136 q^{47} + 35616 q^{48} + 80975 q^{49} + 106212 q^{50} + 29490 q^{51} - 164880 q^{52} - 111818 q^{53} - 34060 q^{54} - 99040 q^{55} - 158592 q^{56} - 42600 q^{57} - 35384 q^{58} - 30532 q^{59} - 35944 q^{60} + 57102 q^{61} + 191100 q^{62} + 18792 q^{63} + 357952 q^{64} + 30276 q^{65} + 155212 q^{66} + 201648 q^{67} - 122336 q^{68} + 101788 q^{69} - 373992 q^{70} + 30392 q^{71} - 45212 q^{72} + 135158 q^{73} - 94996 q^{74} - 78571 q^{75} + 242224 q^{76} + 35024 q^{77} + 213144 q^{78} - 207408 q^{79} + 623368 q^{80} - 498541 q^{81} - 166888 q^{82} - 144900 q^{83} - 5096 q^{84} - 407396 q^{85} - 581168 q^{86} + 125418 q^{87} - 590016 q^{88} - 94782 q^{89} - 63688 q^{90} + 412800 q^{91} - 12752 q^{92} + 495904 q^{93} + 510920 q^{94} + 119624 q^{95} - 9848 q^{96} + 519414 q^{97} + 477736 q^{98} - 141088 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.6.a \(\chi_{48}(1, \cdot)\) 48.6.a.a 1 1
48.6.a.b 1
48.6.a.c 1
48.6.a.d 1
48.6.a.e 1
48.6.c \(\chi_{48}(47, \cdot)\) 48.6.c.a 2 1
48.6.c.b 2
48.6.c.c 2
48.6.c.d 4
48.6.d \(\chi_{48}(25, \cdot)\) None 0 1
48.6.f \(\chi_{48}(23, \cdot)\) None 0 1
48.6.j \(\chi_{48}(13, \cdot)\) 48.6.j.a 40 2
48.6.k \(\chi_{48}(11, \cdot)\) 48.6.k.a 76 2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

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