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Properties

Label 72.7
Level 72
Weight 7
Dimension 375
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 2016
Trace bound 2

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Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(2016\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(72))\).

Total New Old
Modular forms 912 393 519
Cusp forms 816 375 441
Eisenstein series 96 18 78

Trace form

\( 375 q - 8 q^{2} + 6 q^{3} + 18 q^{4} + 124 q^{6} - 314 q^{7} - 806 q^{8} + 66 q^{9} + O(q^{10}) \) \( 375 q - 8 q^{2} + 6 q^{3} + 18 q^{4} + 124 q^{6} - 314 q^{7} - 806 q^{8} + 66 q^{9} + 2248 q^{10} - 10 q^{11} - 3854 q^{12} - 1968 q^{13} - 4398 q^{14} + 9366 q^{15} + 4230 q^{16} + 2438 q^{17} + 16656 q^{18} + 3386 q^{19} - 31830 q^{20} + 3828 q^{21} + 10626 q^{22} + 30882 q^{23} + 23208 q^{24} - 30419 q^{25} + 43920 q^{26} - 22932 q^{27} + 39592 q^{28} + 38556 q^{29} - 128474 q^{30} + 187822 q^{31} - 334058 q^{32} + 36422 q^{33} + 144014 q^{34} - 174924 q^{35} + 85058 q^{36} - 215148 q^{37} + 586970 q^{38} + 259806 q^{39} - 12806 q^{40} + 237680 q^{41} - 321166 q^{42} - 130378 q^{43} - 936094 q^{44} - 185620 q^{45} + 98088 q^{46} + 187590 q^{47} + 388076 q^{48} - 808811 q^{49} + 395950 q^{50} + 222582 q^{51} + 385014 q^{52} + 603624 q^{54} + 735044 q^{55} + 1057200 q^{56} - 758 q^{57} - 127802 q^{58} + 34454 q^{59} - 2117154 q^{60} - 515844 q^{61} - 1346628 q^{62} - 141754 q^{63} - 1377588 q^{64} - 456156 q^{65} + 1724740 q^{66} + 494270 q^{67} + 2326892 q^{68} - 848504 q^{69} - 398578 q^{70} - 796014 q^{72} - 1204482 q^{73} - 1883202 q^{74} + 1326634 q^{75} + 1010966 q^{76} + 48168 q^{77} - 1682150 q^{78} + 396322 q^{79} + 3730896 q^{80} + 954362 q^{81} + 1833104 q^{82} + 553100 q^{83} + 4770152 q^{84} - 857748 q^{85} - 1590334 q^{86} - 1309470 q^{87} - 6555762 q^{88} - 1946698 q^{89} - 9202250 q^{90} - 1959948 q^{91} - 1371594 q^{92} - 1116448 q^{93} + 3995244 q^{94} + 1926396 q^{95} + 6478632 q^{96} + 3380376 q^{97} + 5916862 q^{98} + 3433962 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(72))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
72.7.b \(\chi_{72}(19, \cdot)\) 72.7.b.a 1 1
72.7.b.b 4
72.7.b.c 12
72.7.b.d 12
72.7.e \(\chi_{72}(17, \cdot)\) 72.7.e.a 2 1
72.7.e.b 4
72.7.g \(\chi_{72}(55, \cdot)\) None 0 1
72.7.h \(\chi_{72}(53, \cdot)\) 72.7.h.a 24 1
72.7.j \(\chi_{72}(5, \cdot)\) 72.7.j.a 140 2
72.7.k \(\chi_{72}(7, \cdot)\) None 0 2
72.7.m \(\chi_{72}(41, \cdot)\) 72.7.m.a 36 2
72.7.p \(\chi_{72}(43, \cdot)\) 72.7.p.a 4 2
72.7.p.b 136

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(72)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)