Properties

Label 24.9
Level 24
Weight 9
Dimension 54
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 288
Trace bound 1

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(288\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(24))\).

Total New Old
Modular forms 140 58 82
Cusp forms 116 54 62
Eisenstein series 24 4 20

Trace form

\( 54 q - 6 q^{2} + 56 q^{3} + 660 q^{4} + 226 q^{6} + 1580 q^{7} - 4500 q^{8} + 35318 q^{9} + O(q^{10}) \) \( 54 q - 6 q^{2} + 56 q^{3} + 660 q^{4} + 226 q^{6} + 1580 q^{7} - 4500 q^{8} + 35318 q^{9} + 32628 q^{10} - 39552 q^{11} - 36800 q^{12} + 25232 q^{13} + 121668 q^{14} + 25212 q^{15} - 148576 q^{16} + 77280 q^{17} - 140074 q^{18} + 325488 q^{19} + 354408 q^{20} + 30480 q^{21} + 314880 q^{22} - 366820 q^{24} - 465102 q^{25} - 1703664 q^{26} - 276040 q^{27} + 2881360 q^{28} + 905828 q^{30} + 560044 q^{31} - 2645976 q^{32} - 736612 q^{33} - 7030676 q^{34} - 2415744 q^{35} + 2371308 q^{36} - 3985008 q^{37} + 10249320 q^{38} + 1541040 q^{39} - 16266856 q^{40} - 2187360 q^{41} - 7515764 q^{42} + 10487920 q^{43} + 24238272 q^{44} + 8670592 q^{45} + 8457176 q^{46} + 7530744 q^{48} - 4237438 q^{49} - 26509326 q^{50} - 1728128 q^{51} + 21719360 q^{52} - 935770 q^{54} + 2375416 q^{55} - 1672104 q^{56} + 38748912 q^{57} - 34082300 q^{58} + 44938752 q^{59} + 22110768 q^{60} - 51583600 q^{61} - 19827444 q^{62} - 121901396 q^{63} + 46140528 q^{64} - 52558464 q^{65} + 9830040 q^{66} + 65093232 q^{67} - 35334576 q^{68} + 94226048 q^{69} - 83194232 q^{70} - 15986380 q^{72} - 73020052 q^{73} + 135885720 q^{74} - 130263368 q^{75} - 76512552 q^{76} - 19582960 q^{78} + 224090284 q^{79} + 169182432 q^{80} + 278380854 q^{81} + 63935700 q^{82} - 209328000 q^{83} - 122884520 q^{84} - 264333824 q^{85} - 135445608 q^{86} - 300477828 q^{87} + 189853200 q^{88} - 152224800 q^{89} - 46679572 q^{90} + 777930720 q^{91} - 116843616 q^{92} + 313470352 q^{93} - 438395496 q^{94} + 210201752 q^{96} - 327802900 q^{97} + 230784738 q^{98} - 456201728 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(24))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
24.9.b \(\chi_{24}(19, \cdot)\) 24.9.b.a 16 1
24.9.e \(\chi_{24}(17, \cdot)\) 24.9.e.a 8 1
24.9.g \(\chi_{24}(7, \cdot)\) None 0 1
24.9.h \(\chi_{24}(5, \cdot)\) 24.9.h.a 1 1
24.9.h.b 1
24.9.h.c 28

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(24)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)