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

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

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