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Properties

Label 48.27
Level 48
Weight 27
Dimension 697
Nonzero newspaces 4
Sturm bound 3456
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 27 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(3456\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{27}(\Gamma_1(48))\).

Total New Old
Modular forms 1692 707 985
Cusp forms 1636 697 939
Eisenstein series 56 10 46

Trace form

\( 697 q - q^{3} - 11856952 q^{4} - 1792655268 q^{5} - 26360085956 q^{6} - 32283407510 q^{7} + 2359734612468 q^{8} - 23028024134723 q^{9} + O(q^{10}) \) \( 697 q - q^{3} - 11856952 q^{4} - 1792655268 q^{5} - 26360085956 q^{6} - 32283407510 q^{7} + 2359734612468 q^{8} - 23028024134723 q^{9} + 28841856312640 q^{10} - 94024186657888 q^{11} - 10826366746136 q^{12} - 71727832659634 q^{13} + 1082389570931044 q^{14} - 3521906379936036 q^{15} - 2647822505433584 q^{16} - 1279963673323932 q^{17} + 38602660661408352 q^{18} + 82572758361548062 q^{19} + 99303769531250000 q^{20} + 125272702661142598 q^{21} - 650057057786612808 q^{22} - 1499296629812590208 q^{23} - 2772227753163870356 q^{24} - 6058503247535899527 q^{25} - 7665165814138981300 q^{26} - 1709001850454655817 q^{27} - 23769199964517396480 q^{28} - 44601089997692127508 q^{29} - 82044516616832028084 q^{30} + 14622047360728863346 q^{31} - 68116377477274963040 q^{32} + 142544337360889649860 q^{33} - 293140933429501225208 q^{34} + 225650326976079949536 q^{35} - 989338414314601111088 q^{36} - 1082078599962804614194 q^{37} + 1358665381859109438408 q^{38} - 373186903346568713462 q^{39} - 782661413435820921464 q^{40} + 4165237431624769544196 q^{41} + 1401751438607376936460 q^{42} - 2733316422778470308210 q^{43} + 2843602894225606926040 q^{44} + 1858906487304456855096 q^{45} - 22519406636903750487712 q^{46} + 6514009095056562431968 q^{48} - 270421185811131235068881 q^{49} + 99101310371047225356964 q^{50} + 45920978647609655040128 q^{51} + 62022160431346334206672 q^{52} - 158988060508741728298036 q^{53} + 109113878908588165777780 q^{54} - 74900265894733952217792 q^{55} - 216693862591646989930976 q^{56} + 11808075608193482483470 q^{57} - 247690166222716494054904 q^{58} - 242729923086706756087424 q^{59} - 771493673713928094193608 q^{60} + 705908893467718595997054 q^{61} - 40603961636799652636836 q^{62} - 475507317570769747438470 q^{63} + 2430498855190580659440512 q^{64} + 1931911579280447119423960 q^{65} - 2472681138560781381163652 q^{66} + 530189703029793586809918 q^{67} + 4218180321908281110531392 q^{68} - 878945305656254148697908 q^{69} - 11647932454410766384943592 q^{70} + 2915575753512527620430336 q^{71} + 9548841046118558165310468 q^{72} - 577765833719850720187158 q^{73} - 18579319561956970997553396 q^{74} + 5250497630305817365513899 q^{75} + 11791978739360773317672848 q^{76} - 8143793005809870394674688 q^{77} + 679324826979197068878632 q^{78} - 17540484566582122238104814 q^{79} + 21331903893857185621605672 q^{80} - 129415938154465415757968391 q^{81} - 38495644838337514163215944 q^{82} + 20135076940174270838774240 q^{83} + 11416140495221455019651128 q^{84} - 24015338972652291329451080 q^{85} - 41273366127482810338768560 q^{86} + 63783254233827486196773024 q^{87} - 196018201606714836683645888 q^{88} - 15197034837593106208655340 q^{89} + 122778937509539356191482424 q^{90} + 241876983442949650580523620 q^{91} + 48514182774704744831136496 q^{92} - 83792102102000144098017166 q^{93} - 239367643128474886495901688 q^{94} + 82058142283403344486284296 q^{96} + 125629221258513641599420434 q^{97} + 307338924612720996670418920 q^{98} - 11222582208858620811094532 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{27}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.27.b \(\chi_{48}(7, \cdot)\) None 0 1
48.27.e \(\chi_{48}(17, \cdot)\) 48.27.e.a 1 1
48.27.e.b 8
48.27.e.c 8
48.27.e.d 8
48.27.e.e 26
48.27.g \(\chi_{48}(31, \cdot)\) 48.27.g.a 8 1
48.27.g.b 8
48.27.g.c 10
48.27.h \(\chi_{48}(41, \cdot)\) None 0 1
48.27.i \(\chi_{48}(5, \cdot)\) n/a 412 2
48.27.l \(\chi_{48}(19, \cdot)\) n/a 208 2

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

Decomposition of \(S_{27}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{27}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{27}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 1}\)