Properties

Label 48.19
Level 48
Weight 19
Dimension 481
Nonzero newspaces 4
Sturm bound 2432
Trace bound 1

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 19 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(2432\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(\Gamma_1(48))\).

Total New Old
Modular forms 1180 491 689
Cusp forms 1124 481 643
Eisenstein series 56 10 46

Trace form

\( 481 q - q^{3} + 339656 q^{4} + 5165292 q^{5} - 13365572 q^{6} + 12907082 q^{7} + 33073908 q^{8} - 2279223515 q^{9} + O(q^{10}) \) \( 481 q - q^{3} + 339656 q^{4} + 5165292 q^{5} - 13365572 q^{6} + 12907082 q^{7} + 33073908 q^{8} - 2279223515 q^{9} + 496892480 q^{10} - 5651841760 q^{11} - 24950356376 q^{12} + 17639070078 q^{13} - 73106770844 q^{14} + 22984127964 q^{15} + 268168929296 q^{16} + 169790562708 q^{17} + 588110515680 q^{18} - 1573141350242 q^{19} - 2098468750000 q^{20} + 264884489254 q^{21} + 6523354849208 q^{22} + 9677282270080 q^{23} + 5471139006316 q^{24} - 11788679083087 q^{25} - 4882357630900 q^{26} - 8484443182633 q^{27} + 37614306493440 q^{28} + 13744739262140 q^{29} - 128040339498804 q^{30} + 49274776084242 q^{31} + 40961125409440 q^{32} - 45998928375644 q^{33} + 150676816962312 q^{34} - 25716202410144 q^{35} + 529392858489808 q^{36} - 153742519901058 q^{37} + 102529881407688 q^{38} + 184709334187498 q^{39} - 473104228870264 q^{40} - 188805823569612 q^{41} + 1671051601124620 q^{42} + 2759438848457806 q^{43} - 5138983021336616 q^{44} - 306366207463224 q^{45} + 3389092811074144 q^{46} - 6040717922019872 q^{48} - 24519923296466569 q^{49} - 2394852014509916 q^{50} - 10195765519318912 q^{51} - 23630176039361584 q^{52} + 7500944735878556 q^{53} + 9525748350114676 q^{54} + 5465601923865408 q^{55} - 33091239283146464 q^{56} - 5053823920073906 q^{57} + 30795258094107656 q^{58} + 37364004031220608 q^{59} + 15167466368571192 q^{60} - 84966418628809746 q^{61} - 100228071710679972 q^{62} + 46355290246568730 q^{63} + 76705305969914240 q^{64} - 2847748629987080 q^{65} + 48694938626318332 q^{66} - 18311987882536130 q^{67} - 68437964356846528 q^{68} + 20917936464621708 q^{69} + 95096994302037528 q^{70} + 197043326551167488 q^{71} - 51420445045122300 q^{72} - 113221487105344262 q^{73} + 339308754580001292 q^{74} - 117697183424360181 q^{75} - 186407735168754544 q^{76} - 311924748346588672 q^{77} - 574112143647039832 q^{78} + 407983134112159026 q^{79} + 773262908118305832 q^{80} - 2205937592947870047 q^{81} - 1232845482322873160 q^{82} + 627794169141753440 q^{83} - 716556306856246472 q^{84} + 280833517615025880 q^{85} + 2339091014276103504 q^{86} - 191137374834968160 q^{87} - 1051339464144720832 q^{88} + 124229851967041284 q^{89} - 1557792408548751816 q^{90} - 691730791168739612 q^{91} + 1111890028259949808 q^{92} + 139724544644778386 q^{93} - 1327060054010714616 q^{94} - 2221337979985649656 q^{96} - 3379292665390735390 q^{97} - 3281864229816315416 q^{98} + 2853349087037686012 q^{99} + O(q^{100}) \)

Decomposition of \(S_{19}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.19.b \(\chi_{48}(7, \cdot)\) None 0 1
48.19.e \(\chi_{48}(17, \cdot)\) 48.19.e.a 1 1
48.19.e.b 4
48.19.e.c 6
48.19.e.d 6
48.19.e.e 18
48.19.g \(\chi_{48}(31, \cdot)\) 48.19.g.a 6 1
48.19.g.b 6
48.19.g.c 6
48.19.h \(\chi_{48}(41, \cdot)\) None 0 1
48.19.i \(\chi_{48}(5, \cdot)\) n/a 284 2
48.19.l \(\chi_{48}(19, \cdot)\) n/a 144 2

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

Decomposition of \(S_{19}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{19}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{19}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 1}\)