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Properties

Label 48.7
Level 48
Weight 7
Dimension 157
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 896
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(896\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(48))\).

Total New Old
Modular forms 412 167 245
Cusp forms 356 157 199
Eisenstein series 56 10 46

Trace form

\( 157 q - q^{3} - 184 q^{4} + 132 q^{5} + 508 q^{6} - 358 q^{7} - 1932 q^{8} - 1919 q^{9} + O(q^{10}) \) \( 157 q - q^{3} - 184 q^{4} + 132 q^{5} + 508 q^{6} - 358 q^{7} - 1932 q^{8} - 1919 q^{9} + 2240 q^{10} - 2720 q^{11} + 2344 q^{12} + 4998 q^{13} - 15388 q^{14} - 36 q^{15} + 14096 q^{16} - 7332 q^{17} + 14880 q^{18} - 14882 q^{19} - 14000 q^{20} + 2422 q^{21} - 83272 q^{22} + 26240 q^{23} + 84844 q^{24} - 42427 q^{25} - 5300 q^{26} - 47353 q^{27} - 69120 q^{28} + 121780 q^{29} - 160884 q^{30} + 34050 q^{31} - 52960 q^{32} - 524 q^{33} + 250632 q^{34} + 162336 q^{35} + 204496 q^{36} + 63942 q^{37} + 16968 q^{38} - 47174 q^{39} - 473464 q^{40} - 129924 q^{41} - 10100 q^{42} + 200686 q^{43} - 193192 q^{44} - 124704 q^{45} - 299552 q^{46} + 111328 q^{48} + 135395 q^{49} + 537764 q^{50} + 545408 q^{51} + 1003856 q^{52} + 363796 q^{53} + 230644 q^{54} + 422208 q^{55} - 420448 q^{56} - 110546 q^{57} - 1477624 q^{58} - 886144 q^{59} - 385608 q^{60} - 1378986 q^{61} - 719652 q^{62} + 12810 q^{63} - 443776 q^{64} + 296360 q^{65} + 1264828 q^{66} - 65090 q^{67} + 3197632 q^{68} + 408108 q^{69} + 989208 q^{70} + 534016 q^{71} - 820860 q^{72} - 33902 q^{73} - 4894836 q^{74} + 732699 q^{75} - 3522544 q^{76} - 860672 q^{77} + 1140968 q^{78} + 1757538 q^{79} + 4668072 q^{80} - 2701539 q^{81} + 2664760 q^{82} - 2497760 q^{83} + 581560 q^{84} + 1261320 q^{85} + 4142928 q^{86} - 1841760 q^{87} - 1534912 q^{88} - 3515412 q^{89} - 799176 q^{90} + 1145764 q^{91} - 9470992 q^{92} - 1935934 q^{93} - 6463224 q^{94} + 3835400 q^{96} + 645530 q^{97} + 12708584 q^{98} - 1337732 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.7.b \(\chi_{48}(7, \cdot)\) None 0 1
48.7.e \(\chi_{48}(17, \cdot)\) 48.7.e.a 1 1
48.7.e.b 2
48.7.e.c 2
48.7.e.d 6
48.7.g \(\chi_{48}(31, \cdot)\) 48.7.g.a 2 1
48.7.g.b 2
48.7.g.c 2
48.7.h \(\chi_{48}(41, \cdot)\) None 0 1
48.7.i \(\chi_{48}(5, \cdot)\) 48.7.i.a 92 2
48.7.l \(\chi_{48}(19, \cdot)\) 48.7.l.a 48 2

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)