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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

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

Display 100 coefficients 10 coefficients

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 available 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

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