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Properties

Label 32.10
Level 32
Weight 10
Dimension 157
Nonzero newspaces 3
Newform subspaces 7
Sturm bound 640
Trace bound 1

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Defining parameters

Level: \( N \) = \( 32 = 2^{5} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 7 \)
Sturm bound: \(640\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(32))\).

Total New Old
Modular forms 304 167 137
Cusp forms 272 157 115
Eisenstein series 32 10 22

Trace form

\( 157 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 714 q^{5} - 4 q^{6} - 4804 q^{7} - 4 q^{8} + 47417 q^{9} + O(q^{10}) \) \( 157 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 714 q^{5} - 4 q^{6} - 4804 q^{7} - 4 q^{8} + 47417 q^{9} - 45004 q^{10} - 4 q^{11} - 231988 q^{12} - 108462 q^{13} + 221100 q^{14} + 163136 q^{15} + 566096 q^{16} - 650206 q^{17} - 2230744 q^{18} - 4 q^{19} + 1809996 q^{20} + 2672124 q^{21} - 270560 q^{22} - 6878012 q^{23} - 9360432 q^{24} + 4437435 q^{25} + 1052976 q^{26} - 12650092 q^{27} + 10895736 q^{28} - 2814398 q^{29} - 22129596 q^{30} + 21360912 q^{31} - 14720664 q^{32} + 7039128 q^{33} + 19270544 q^{34} - 38240620 q^{35} + 28519216 q^{36} - 21033526 q^{37} + 6664084 q^{38} + 89864404 q^{39} + 4161768 q^{40} - 23699994 q^{41} - 10757624 q^{42} - 38062460 q^{43} - 151593084 q^{44} + 31949022 q^{45} + 113136476 q^{46} - 7432320 q^{47} + 220309488 q^{48} + 80994889 q^{49} - 23597484 q^{50} + 180107384 q^{51} - 261806044 q^{52} - 66507670 q^{53} - 426123872 q^{54} - 147165668 q^{55} + 539054504 q^{56} + 191860508 q^{57} + 719447072 q^{58} + 288075228 q^{59} - 480303368 q^{60} - 99083166 q^{61} - 95586312 q^{62} - 406920048 q^{63} - 715478824 q^{64} - 196035572 q^{65} - 386126836 q^{66} + 503547476 q^{67} + 1273611856 q^{68} - 17875684 q^{69} + 1332494744 q^{70} - 322133220 q^{71} - 1728136492 q^{72} - 371660714 q^{73} - 2309233812 q^{74} - 1146770576 q^{75} - 428646404 q^{76} + 393394572 q^{77} + 3057328692 q^{78} + 248943744 q^{79} + 3122020024 q^{80} + 1129261945 q^{81} - 1434329604 q^{82} + 2478583716 q^{83} - 6193102112 q^{84} - 2289203668 q^{85} - 1286692416 q^{86} - 2891479052 q^{87} + 1844752480 q^{88} - 1524808218 q^{89} + 7292132840 q^{90} - 1091566804 q^{91} + 4308804008 q^{92} + 2011726960 q^{93} - 7541285080 q^{94} + 6678085496 q^{95} - 10602864256 q^{96} + 1805896106 q^{97} + 4250531736 q^{98} - 1556903760 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.10.a \(\chi_{32}(1, \cdot)\) 32.10.a.a 1 1
32.10.a.b 2
32.10.a.c 2
32.10.a.d 2
32.10.a.e 2
32.10.b \(\chi_{32}(17, \cdot)\) 32.10.b.a 8 1
32.10.e \(\chi_{32}(9, \cdot)\) None 0 2
32.10.g \(\chi_{32}(5, \cdot)\) 32.10.g.a 140 4

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(32)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)