# Properties

 Label 48.28.j Level $48$ Weight $28$ Character orbit 48.j Rep. character $\chi_{48}(13,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $216$ Sturm bound $224$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$48 = 2^{4} \cdot 3$$ Weight: $$k$$ $$=$$ $$28$$ Character orbit: $$[\chi]$$ $$=$$ 48.j (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Sturm bound: $$224$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{28}(48, [\chi])$$.

Total New Old
Modular forms 436 216 220
Cusp forms 428 216 212
Eisenstein series 8 0 8

## Trace form

 $$216 q - 250191380 q^{4} + 574361867604 q^{8} + O(q^{10})$$ $$216 q - 250191380 q^{4} + 574361867604 q^{8} + 40326868591752 q^{10} + 68079643620440 q^{11} - 844505508195864 q^{12} + 14310437170500228 q^{14} + 15569560546875000 q^{15} - 15162632769106368 q^{16} + 84176428770943164 q^{18} + 361273435637780376 q^{19} + 1506192207031250000 q^{20} + 3156611586865402304 q^{22} - 8867015560102411548 q^{24} - 16920893255094036020 q^{26} + 53875738274858921896 q^{28} + 54243547129728547600 q^{29} + 139034526412991320872 q^{30} - 586021111138681022184 q^{31} + 1169600394941455275840 q^{32} - 328613542601185531328 q^{34} + 2996664838584338597304 q^{35} + 604727236419344930412 q^{36} + 940972239156445764496 q^{37} + 1297404346755636263336 q^{38} + 21152560586798995589584 q^{40} + 26008127252247890350260 q^{42} - 47464778955337323971240 q^{43} - 52461449140051092163016 q^{44} + 99449147843179593540392 q^{46} + 146829178022751507655152 q^{48} - 2027695752931914930020184 q^{49} - 530329619151843324195612 q^{50} + 53439033226967889256296 q^{51} + 1174180369006644733245168 q^{52} + 11942680219833823794032 q^{53} - 82850437548319950802548 q^{54} - 1763984545166965006302144 q^{56} + 2830268743847357022274576 q^{58} - 2350600637400307436273504 q^{59} - 1668323162834136219042504 q^{60} + 2475467954128860415560432 q^{61} + 8665698329608506792900924 q^{62} - 1970230917553329251359224 q^{63} - 10262726898362787826139960 q^{64} - 5823043807854969859362224 q^{65} - 3270547759318301297192472 q^{66} - 23062703446363715515682256 q^{67} + 8855668157442147356761312 q^{68} + 11740592568227105262742128 q^{69} + 28215717304228108647550240 q^{70} - 6493344714991210700840292 q^{72} - 87906462349433607289606612 q^{74} + 12798775084238306951428944 q^{75} + 69890107187390521634742184 q^{76} - 87016675797172706151206416 q^{77} + 24662557612219322602480572 q^{78} + 121084648451037149651550568 q^{79} + 113202077632773448639507912 q^{80} - 1395593688072961432569364056 q^{81} + 316375174117474717224830360 q^{82} + 346714043299972995691327480 q^{83} - 68120707589457819419287800 q^{84} - 224109186421427402343750000 q^{85} + 864024318743526433798324432 q^{86} + 467674338009523891230892704 q^{88} - 84973893550143596833739832 q^{90} + 467054745940218004291558616 q^{91} - 1017412224654144957499163984 q^{92} + 581213094484509431967632344 q^{94} + 2806712915077339924415470032 q^{95} + 1302540090312238806672636480 q^{96} - 922979840679433969910083160 q^{98} + 173049319723612841075444760 q^{99} + O(q^{100})$$

## Decomposition of $$S_{28}^{\mathrm{new}}(48, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{28}^{\mathrm{old}}(48, [\chi])$$ into lower level spaces

$$S_{28}^{\mathrm{old}}(48, [\chi]) \simeq$$ $$S_{28}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 2}$$