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Properties

Label 32.18
Level 32
Weight 18
Dimension 301
Nonzero newspaces 3
Sturm bound 1152
Trace bound 1

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Defining parameters

Level: \( N \) = \( 32 = 2^{5} \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 3 \)
Sturm bound: \(1152\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(32))\).

Total New Old
Modular forms 560 311 249
Cusp forms 528 301 227
Eisenstein series 32 10 22

Trace form

\( 301 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 24474 q^{5} - 4 q^{6} - 11529604 q^{7} - 4 q^{8} - 30609799 q^{9} + O(q^{10}) \) \( 301 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 24474 q^{5} - 4 q^{6} - 11529604 q^{7} - 4 q^{8} - 30609799 q^{9} - 1278125004 q^{10} - 4 q^{11} + 1820388812 q^{12} + 2032852642 q^{13} - 15489927252 q^{14} + 9993282176 q^{15} - 45972879024 q^{16} - 41396936638 q^{17} + 233313227816 q^{18} - 4 q^{19} - 390368750004 q^{20} + 619542486012 q^{21} + 530246914848 q^{22} - 1300804214396 q^{23} - 494169400368 q^{24} + 1917034764155 q^{25} + 3622860188976 q^{26} + 6664762540820 q^{27} - 1361371417224 q^{28} + 3425269494418 q^{29} - 441467853756 q^{30} + 20788364657168 q^{31} - 1461088963224 q^{32} - 5242062274248 q^{33} + 10549078818704 q^{34} + 52420460186900 q^{35} - 9682157690576 q^{36} - 4242909100646 q^{37} + 110396316477844 q^{38} + 141005782882708 q^{39} - 332515267943192 q^{40} - 48982284778554 q^{41} + 396390543723016 q^{42} + 162504227708164 q^{43} - 394621005463164 q^{44} - 299705765052498 q^{45} + 200154007036764 q^{46} + 376698804821760 q^{47} + 493902287686128 q^{48} + 175975805586585 q^{49} - 2500030748018604 q^{50} + 424338171937016 q^{51} + 2897328057919524 q^{52} + 3082250486397626 q^{53} - 2604398545366112 q^{54} + 866241923650652 q^{55} + 1115181228092840 q^{56} + 3151954554369596 q^{57} - 1625954879790048 q^{58} + 1130082973621212 q^{59} + 5119052776807672 q^{60} - 3431326460543310 q^{61} - 9816242000697864 q^{62} - 1795134603361968 q^{63} - 8897159508411688 q^{64} - 3016974559891412 q^{65} - 1590876896828404 q^{66} + 8266854410067156 q^{67} + 11216904082927696 q^{68} + 23043765335804444 q^{69} - 39022304411881576 q^{70} + 3342884290952796 q^{71} + 58445013566266580 q^{72} + 26743252577886390 q^{73} - 11178105501721236 q^{74} - 40090559506028816 q^{75} - 26524159112622084 q^{76} - 55706577529171188 q^{77} + 122101139928172596 q^{78} + 45299671392008448 q^{79} + 125552032376763064 q^{80} + 16470433639321321 q^{81} - 137878855652339204 q^{82} + 112690648594272036 q^{83} + 6275063701155040 q^{84} + 101565217449394252 q^{85} + 221367316838442432 q^{86} + 37908631977310132 q^{87} - 260759398451877280 q^{88} + 30942047730543558 q^{89} - 89790578058981400 q^{90} - 207948447056288212 q^{91} + 707582779477728680 q^{92} + 103559726119819504 q^{93} - 160980922394225368 q^{94} + 330798631666796216 q^{95} - 348145823362502272 q^{96} + 275531683337771850 q^{97} + 429601535477765016 q^{98} - 576117491877486288 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.18.a \(\chi_{32}(1, \cdot)\) 32.18.a.a 1 1
32.18.a.b 2
32.18.a.c 2
32.18.a.d 4
32.18.a.e 4
32.18.a.f 4
32.18.b \(\chi_{32}(17, \cdot)\) 32.18.b.a 16 1
32.18.e \(\chi_{32}(9, \cdot)\) None 0 2
32.18.g \(\chi_{32}(5, \cdot)\) n/a 268 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(32)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)