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Properties

Label 32.6
Level 32
Weight 6
Dimension 85
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 384
Trace bound 1

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Defining parameters

Level: \( N \) = \( 32 = 2^{5} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(384\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(32))\).

Total New Old
Modular forms 176 95 81
Cusp forms 144 85 59
Eisenstein series 32 10 22

Trace form

\( 85 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 34 q^{5} - 4 q^{6} - 100 q^{7} - 4 q^{8} + 281 q^{9} + O(q^{10}) \) \( 85 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 34 q^{5} - 4 q^{6} - 100 q^{7} - 4 q^{8} + 281 q^{9} - 204 q^{10} - 4 q^{11} - 1588 q^{12} + 106 q^{13} + 2476 q^{14} + 416 q^{15} + 4176 q^{16} + 1810 q^{17} - 1624 q^{18} - 4 q^{19} - 7604 q^{20} - 5892 q^{21} - 12384 q^{22} - 668 q^{23} + 21456 q^{24} - 2725 q^{25} + 12976 q^{26} - 7468 q^{27} - 2184 q^{28} + 3674 q^{29} - 32316 q^{30} + 35984 q^{31} - 18584 q^{32} + 10824 q^{33} - 6256 q^{34} - 4780 q^{35} + 65584 q^{36} - 7262 q^{37} + 404 q^{38} - 80012 q^{39} - 28952 q^{40} - 35338 q^{41} - 53624 q^{42} + 32068 q^{43} + 3716 q^{44} + 64182 q^{45} + 63324 q^{46} + 54720 q^{47} + 112368 q^{48} + 67617 q^{49} - 4524 q^{50} - 19912 q^{51} + 18468 q^{52} - 125950 q^{53} + 1312 q^{54} + 24572 q^{55} - 80984 q^{56} - 135028 q^{57} - 84576 q^{58} - 28964 q^{59} - 46088 q^{60} + 204666 q^{61} + 63480 q^{62} - 5328 q^{63} - 49192 q^{64} + 93948 q^{65} - 145012 q^{66} - 61164 q^{67} - 151216 q^{68} - 271204 q^{69} - 56296 q^{70} - 62852 q^{71} + 27092 q^{72} - 80346 q^{73} + 213100 q^{74} + 205744 q^{75} + 255996 q^{76} + 180428 q^{77} + 83508 q^{78} + 247872 q^{79} - 97096 q^{80} + 299713 q^{81} + 435196 q^{82} - 329244 q^{83} + 597472 q^{84} - 118628 q^{85} + 269888 q^{86} - 590060 q^{87} - 199840 q^{88} - 259338 q^{89} - 706840 q^{90} + 200108 q^{91} - 650328 q^{92} + 151600 q^{93} - 261592 q^{94} + 837336 q^{95} - 501376 q^{96} + 260058 q^{97} - 395624 q^{98} + 338544 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.6.a \(\chi_{32}(1, \cdot)\) 32.6.a.a 1 1
32.6.a.b 1
32.6.a.c 1
32.6.a.d 2
32.6.b \(\chi_{32}(17, \cdot)\) 32.6.b.a 4 1
32.6.e \(\chi_{32}(9, \cdot)\) None 0 2
32.6.g \(\chi_{32}(5, \cdot)\) 32.6.g.a 76 4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(32)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)