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Properties

Label 48.25
Level 48
Weight 25
Dimension 643
Nonzero newspaces 4
Sturm bound 3200
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 25 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(3200\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{25}(\Gamma_1(48))\).

Total New Old
Modular forms 1564 653 911
Cusp forms 1508 643 865
Eisenstein series 56 10 46

Trace form

\( 643 q - q^{3} - 50616184 q^{4} + 726053328 q^{5} + 5313898588 q^{6} - 15804565918 q^{7} - 267070377420 q^{8} - 2068772711609 q^{9} + O(q^{10}) \) \( 643 q - q^{3} - 50616184 q^{4} + 726053328 q^{5} + 5313898588 q^{6} - 15804565918 q^{7} - 267070377420 q^{8} - 2068772711609 q^{9} - 2342804699008 q^{10} - 1634730238080 q^{11} - 11448229457912 q^{12} - 81855276426006 q^{13} - 135467353557468 q^{14} + 103282844659452 q^{15} - 189123729077104 q^{16} - 343299546429840 q^{17} + 1066194003372096 q^{18} - 9363723036286082 q^{19} - 17586105468750000 q^{20} - 13947477023430818 q^{21} - 85765565566734664 q^{22} - 131693982218196480 q^{23} - 74082572204620436 q^{24} - 346454066504482345 q^{25} - 113815533226821300 q^{26} - 224598147779641441 q^{27} + 529000294123941120 q^{28} + 1347931431204725520 q^{29} + 4239473344997521644 q^{30} - 1517055842079350502 q^{31} - 1935013230625456800 q^{32} - 2109904323252560804 q^{33} + 13892396924577475080 q^{34} - 13284910666843161984 q^{35} + 9131263750455870544 q^{36} + 14517749297962239594 q^{37} - 71912761598966513400 q^{38} + 12272882419896880738 q^{39} + 89464698289596515336 q^{40} - 34084325750269865616 q^{41} + 21257550194926318540 q^{42} - 19579746074246241602 q^{43} + 103692341107014322968 q^{44} - 128394707292180376884 q^{45} + 564461476950727313824 q^{46} + 51251734297118156128 q^{48} - 3257676375927330234079 q^{49} + 214676476192408250916 q^{50} - 1900618843919107686400 q^{51} + 5690700234471408305936 q^{52} - 1232676980202520301040 q^{53} - 3659689894681723910156 q^{54} + 2288204168507016463872 q^{55} + 446936000543095942368 q^{56} - 391551608629725616322 q^{57} - 719983130528527347064 q^{58} + 297323798657615847936 q^{59} - 4595575123058346314760 q^{60} + 2833339178831636608554 q^{61} - 6594580955125897729380 q^{62} + 33511221762125727522 q^{63} - 48047354754196124598016 q^{64} - 5807134755655595625312 q^{65} + 19628615678774743683868 q^{66} - 31768211176011575481602 q^{67} - 62278259170849213282560 q^{68} - 19141851384626216939844 q^{69} + 251594968254779430059544 q^{70} + 90693589060095558211584 q^{71} - 140913931459238046895164 q^{72} + 42119969602426354929358 q^{73} + 100154129719318977596364 q^{74} + 202585651296333952950243 q^{75} - 309147817215478607931184 q^{76} - 156416145917021713935360 q^{77} + 359935007792725523336456 q^{78} + 7142982942873300522138 q^{79} + 68426355556221262824168 q^{80} - 1606406026261127347939581 q^{81} + 115213083578224729587832 q^{82} - 397141287297367996656000 q^{83} - 96347715999278868910856 q^{84} - 411894868232378624829024 q^{85} - 933090932058551293465008 q^{86} - 532685024752517787790080 q^{87} + 1639266825881837672768576 q^{88} - 387763328863741596856272 q^{89} - 242911740861575312817864 q^{90} - 793400982512301255695228 q^{91} + 838236494816370319993200 q^{92} + 1450495488538968670662554 q^{93} + 2540318044641033104799624 q^{94} + 824317409818026121797896 q^{96} - 80432707194063339654010 q^{97} + 3513070353466033747972200 q^{98} - 1729371524283878918510852 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{25}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.25.b \(\chi_{48}(7, \cdot)\) None 0 1
48.25.e \(\chi_{48}(17, \cdot)\) 48.25.e.a 1 1
48.25.e.b 6
48.25.e.c 8
48.25.e.d 8
48.25.e.e 24
48.25.g \(\chi_{48}(31, \cdot)\) 48.25.g.a 8 1
48.25.g.b 8
48.25.g.c 8
48.25.h \(\chi_{48}(41, \cdot)\) None 0 1
48.25.i \(\chi_{48}(5, \cdot)\) n/a 380 2
48.25.l \(\chi_{48}(19, \cdot)\) n/a 192 2

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

Decomposition of \(S_{25}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{25}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{25}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{25}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{25}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{25}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{25}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{25}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{25}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)