Properties

Label 9.24
Level 9
Weight 24
Dimension 53
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 144
Trace bound 1

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 24 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(144\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 73 58 15
Cusp forms 65 53 12
Eisenstein series 8 5 3

Trace form

\( 53 q - 3015 q^{2} - 162336 q^{3} - 57218701 q^{4} - 98648100 q^{5} - 922041945 q^{6} + 5937165712 q^{7} - 41232495798 q^{8} - 15707798892 q^{9} + O(q^{10}) \) \( 53 q - 3015 q^{2} - 162336 q^{3} - 57218701 q^{4} - 98648100 q^{5} - 922041945 q^{6} + 5937165712 q^{7} - 41232495798 q^{8} - 15707798892 q^{9} + 886733453472 q^{10} - 1732224616848 q^{11} + 7026776146932 q^{12} - 7724179531136 q^{13} - 40779482938848 q^{14} + 102746096401032 q^{15} - 301901912365681 q^{16} + 82932756601518 q^{17} - 1015637709578004 q^{18} - 145606453279364 q^{19} - 1509681870665388 q^{20} - 1271308283377674 q^{21} - 3373321834359609 q^{22} - 5667112721607840 q^{23} + 33161190854087277 q^{24} - 29971227849068329 q^{25} + 43292371137368436 q^{26} + 31441379169979512 q^{27} + 96173123420433724 q^{28} - 80198133387488676 q^{29} + 330990272769168 q^{30} + 10436066240274736 q^{31} + 31203740622081807 q^{32} - 929357005571791038 q^{33} + 2330222793472146357 q^{34} - 2541607389818978904 q^{35} - 1123405663575587085 q^{36} + 4423726293911833030 q^{37} - 10821157763329244925 q^{38} + 2712286427477886624 q^{39} + 10315318806793500456 q^{40} - 16175339272259639172 q^{41} + 11934917111168297586 q^{42} + 8819724105167498344 q^{43} - 19631012865607533654 q^{44} + 15901630393312558890 q^{45} + 61056849244633119528 q^{46} - 17306698752604817280 q^{47} - 40480058382647533725 q^{48} - 14421726272417991435 q^{49} + 160263558040082413329 q^{50} - 178319943871935954552 q^{51} - 228146084143819259150 q^{52} + 430721227430367172866 q^{53} - 113698830373567787655 q^{54} - 587008037687789944776 q^{55} + 279682617934344062574 q^{56} + 226240579268459200920 q^{57} - 325784149228055784444 q^{58} - 112606891133035666752 q^{59} - 953628633609756094116 q^{60} + 295731817468160340304 q^{61} + 2860653331561306123620 q^{62} - 68499165113084132064 q^{63} + 2026178088325993999106 q^{64} - 2300308291049009165730 q^{65} + 3571588029002089420170 q^{66} + 750407710324079121352 q^{67} - 8113177844693934915609 q^{68} - 6641159390196078076074 q^{69} + 5511809943722998488162 q^{70} + 271492216073982791496 q^{71} + 9630260525966953701195 q^{72} - 1451638965651846261950 q^{73} - 25218805577215148069004 q^{74} + 16394554011602186361312 q^{75} + 21587485487040073841149 q^{76} - 19898757600989565460338 q^{77} - 62516515852228971184362 q^{78} - 1719997192864958549120 q^{79} + 125398871682175408299552 q^{80} - 4457129282696628137772 q^{81} - 63478951928000884940826 q^{82} - 49962647131561018277640 q^{83} + 157363438547234314093098 q^{84} + 41973938954476105014576 q^{85} - 87402709741869520684479 q^{86} - 108494475880475744101872 q^{87} - 72898540705024208113269 q^{88} + 145066211395007707384326 q^{89} + 108434693280500456315724 q^{90} - 146353351643813694421864 q^{91} + 33092796337743376367298 q^{92} + 172144963592860836762462 q^{93} - 94863907829601227929560 q^{94} - 116628784048590266497248 q^{95} - 624214773059653515520152 q^{96} + 282351826312972414675912 q^{97} + 288157453461003884113368 q^{98} + 23801989380986068508916 q^{99} + O(q^{100}) \)

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

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
9.24.a \(\chi_{9}(1, \cdot)\) 9.24.a.a 1 1
9.24.a.b 2
9.24.a.c 2
9.24.a.d 4
9.24.c \(\chi_{9}(4, \cdot)\) 9.24.c.a 44 2

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

\( S_{24}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)