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Properties

Label 48.24.j
Level $48$
Weight $24$
Character orbit 48.j
Rep. character $\chi_{48}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $184$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 48.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(48, [\chi])\).

Total New Old
Modular forms 372 184 188
Cusp forms 364 184 180
Eisenstein series 8 0 8

Trace form

\( 184 q + 20101996 q^{4} - 61280246316 q^{8} + O(q^{10}) \) \( 184 q + 20101996 q^{4} - 61280246316 q^{8} + 835904008712 q^{10} - 1951148533352 q^{11} + 4225099084776 q^{12} + 24161501993988 q^{14} + 69198046875000 q^{15} + 186202903548864 q^{16} + 121381938567612 q^{18} - 33497748322216 q^{19} - 1872342968750000 q^{20} - 9146550060838080 q^{22} + 1201218622667748 q^{24} - 59838318056660020 q^{26} - 128030159231913176 q^{28} - 80364689641708336 q^{29} - 244343736767170008 q^{30} - 609803445513715944 q^{31} - 532722654506952000 q^{32} - 3126894471328298304 q^{34} + 191164112099572344 q^{35} + 484413475605851628 q^{36} + 2494663215477821008 q^{37} - 3392793966871378904 q^{38} - 16510953711606587056 q^{40} + 9039714404795268660 q^{42} + 8018619605053707416 q^{43} - 85145389869359997256 q^{44} - 16130897754741901528 q^{46} - 55841301297104218128 q^{48} - 719407072939269801016 q^{49} - 59010837258340312092 q^{50} + 51839399036128705704 q^{51} + 109818910077638332528 q^{52} - 27281061994464291152 q^{53} + 49119859166084601228 q^{54} - 90379237811130289728 q^{56} - 670184311379550153968 q^{58} - 974343219256056248416 q^{59} + 202454426814254552376 q^{60} + 689547400664843490608 q^{61} - 953585531691197894724 q^{62} - 496404867108422587896 q^{63} + 3146353407876442961224 q^{64} - 1355511643942627399024 q^{65} + 1079452266612305127912 q^{66} + 3469258319679421444528 q^{67} - 2082038477856096624544 q^{68} + 1740473287449277893552 q^{69} + 4085815459523185244320 q^{70} + 2260156093898587530012 q^{72} + 5481770393543905675180 q^{74} - 2994731501585309691696 q^{75} + 3622586920419311433256 q^{76} + 10948512166470615038512 q^{77} + 20830680824378792075964 q^{78} + 7657079036735452154472 q^{79} - 22277011318884806383288 q^{80} - 181197846001784466850104 q^{81} + 29199736756329469254680 q^{82} + 19498160568522243786680 q^{83} - 28675429455472378721784 q^{84} + 25986907556994531250000 q^{85} + 79497921536638972529360 q^{86} - 60708335494759095431264 q^{88} - 22184865142961105533752 q^{90} - 158210290006197991730920 q^{91} + 165179375591045694834608 q^{92} - 229557499516239312083240 q^{94} - 472381559010145697978928 q^{95} - 74615531778439700443200 q^{96} + 814587015432048047125160 q^{98} - 61229108431132036579368 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{24}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{24}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{24}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{24}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)