Properties

Label 5.12
Level 5
Weight 12
Dimension 7
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 24
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(24\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(5))\).

Total New Old
Modular forms 13 9 4
Cusp forms 9 7 2
Eisenstein series 4 2 2

Trace form

\( 7q + 14q^{2} - 1012q^{3} + 6012q^{4} - 3425q^{5} + 31504q^{6} + 40344q^{7} - 346200q^{8} + 454723q^{9} + O(q^{10}) \) \( 7q + 14q^{2} - 1012q^{3} + 6012q^{4} - 3425q^{5} + 31504q^{6} + 40344q^{7} - 346200q^{8} + 454723q^{9} + 260150q^{10} - 1413316q^{11} - 1220576q^{12} + 3040218q^{13} + 1818264q^{14} + 1645700q^{15} - 5401168q^{16} - 2406346q^{17} + 2755958q^{18} + 20406740q^{19} + 10859900q^{20} - 63279336q^{21} - 105430632q^{22} + 26485848q^{23} + 275764320q^{24} + 188449375q^{25} - 419449996q^{26} - 242961400q^{27} + 179345712q^{28} + 380079610q^{29} + 117768400q^{30} - 268050976q^{31} - 476025056q^{32} - 70979744q^{33} + 584514364q^{34} + 158492400q^{35} - 772438948q^{36} - 270337326q^{37} + 928850600q^{38} - 321965704q^{39} + 181921000q^{40} + 458473294q^{41} + 1902541008q^{42} - 1129907292q^{43} - 1378140656q^{44} - 1294625525q^{45} + 3670019704q^{46} + 221408384q^{47} - 5130637952q^{48} - 5511437393q^{49} - 4484451250q^{50} + 13942147384q^{51} + 13174967064q^{52} + 493431938q^{53} - 22959047360q^{54} - 7305926100q^{55} + 8131081920q^{56} + 5021442800q^{57} + 9757106100q^{58} + 11444056220q^{59} + 10152654400q^{60} - 14725486366q^{61} - 22735073952q^{62} - 10750886232q^{63} + 3780862912q^{64} - 8608720550q^{65} - 7362926752q^{66} + 19529964204q^{67} - 1251711608q^{68} + 52825715016q^{69} + 34748023800q^{70} - 50363939096q^{71} - 63347763000q^{72} - 20102028402q^{73} + 53336626564q^{74} + 9449727500q^{75} - 53974552560q^{76} - 26504706672q^{77} + 120428573776q^{78} + 50566058960q^{79} + 48367377200q^{80} - 30124770233q^{81} - 68124845412q^{82} + 16503964428q^{83} - 104885035296q^{84} - 61874541850q^{85} - 77495824096q^{86} - 21134853400q^{87} - 33934826400q^{88} + 168774049830q^{89} + 123557259950q^{90} + 148769636064q^{91} + 232124189904q^{92} - 301987859184q^{93} - 271190537336q^{94} - 282533715500q^{95} + 299296601984q^{96} + 123413770134q^{97} + 73456940302q^{98} + 27251190476q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.12.a \(\chi_{5}(1, \cdot)\) 5.12.a.a 1 1
5.12.a.b 2
5.12.b \(\chi_{5}(4, \cdot)\) 5.12.b.a 4 1

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(5))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(5)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)