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Properties

Label 24.7
Level 24
Weight 7
Dimension 40
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 224
Trace bound 1

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(224\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(24))\).

Total New Old
Modular forms 108 44 64
Cusp forms 84 40 44
Eisenstein series 24 4 20

Trace form

\( 40 q + 10 q^{2} - 10 q^{3} - 44 q^{4} - 158 q^{6} + 152 q^{7} + 796 q^{8} + 2840 q^{9} + O(q^{10}) \) \( 40 q + 10 q^{2} - 10 q^{3} - 44 q^{4} - 158 q^{6} + 152 q^{7} + 796 q^{8} + 2840 q^{9} + 1748 q^{10} + 2720 q^{11} - 464 q^{12} + 156 q^{13} - 6444 q^{14} + 1452 q^{15} + 13600 q^{16} - 4888 q^{17} + 470 q^{18} - 564 q^{19} - 31608 q^{20} - 15108 q^{21} - 70144 q^{22} + 34220 q^{24} + 37908 q^{25} + 53952 q^{26} + 37574 q^{27} - 47344 q^{28} - 39772 q^{30} - 135496 q^{31} + 109480 q^{32} - 62524 q^{33} - 29844 q^{34} + 162336 q^{35} + 78348 q^{36} + 171132 q^{37} - 89080 q^{38} + 74700 q^{39} + 154808 q^{40} - 54280 q^{41} + 56380 q^{42} - 340884 q^{43} + 229184 q^{44} - 355136 q^{45} + 102456 q^{46} - 6600 q^{48} + 484128 q^{49} - 500078 q^{50} + 532576 q^{51} + 197280 q^{52} - 87850 q^{54} - 694376 q^{55} - 699816 q^{56} - 907164 q^{57} - 797404 q^{58} - 886144 q^{59} + 457968 q^{60} + 592092 q^{61} + 691356 q^{62} + 794488 q^{63} - 130064 q^{64} + 473376 q^{65} + 749496 q^{66} + 995052 q^{67} + 669104 q^{68} - 981184 q^{69} + 1259560 q^{70} - 774364 q^{72} + 1418096 q^{73} - 753720 q^{74} - 551642 q^{75} - 2236680 q^{76} - 1576000 q^{78} + 41144 q^{79} - 251616 q^{80} - 631416 q^{81} + 1057332 q^{82} + 2497760 q^{83} + 680152 q^{84} + 197376 q^{85} + 476024 q^{86} + 2102604 q^{87} + 2072144 q^{88} + 367400 q^{89} + 3210284 q^{90} - 3636168 q^{91} - 377376 q^{92} + 354652 q^{93} + 1503096 q^{94} - 1136296 q^{96} - 3444592 q^{97} + 182674 q^{98} - 2188640 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(24))\)

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
24.7.b \(\chi_{24}(19, \cdot)\) 24.7.b.a 12 1
24.7.e \(\chi_{24}(17, \cdot)\) 24.7.e.a 6 1
24.7.g \(\chi_{24}(7, \cdot)\) None 0 1
24.7.h \(\chi_{24}(5, \cdot)\) 24.7.h.a 1 1
24.7.h.b 1
24.7.h.c 20

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

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