# Properties

 Label 48.28.k Level $48$ Weight $28$ Character orbit 48.k Rep. character $\chi_{48}(11,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $428$ Sturm bound $224$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$48 = 2^{4} \cdot 3$$ Weight: $$k$$ $$=$$ $$28$$ Character orbit: $$[\chi]$$ $$=$$ 48.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$48$$ 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 436 436 0
Cusp forms 428 428 0
Eisenstein series 8 8 0

## Trace form

 $$428 q - 2 q^{3} - 4 q^{4} + 59499919468 q^{6} - 8 q^{7} + O(q^{10})$$ $$428 q - 2 q^{3} - 4 q^{4} + 59499919468 q^{6} - 8 q^{7} - 56821289062504 q^{10} - 904484200688720 q^{12} - 4 q^{13} + 103295644994347664 q^{16} + 67514503723450612 q^{18} + 361273435637780372 q^{19} - 15251194969976 q^{21} + 5782296847474979960 q^{22} + 24054204993847404936 q^{24} + 16968274332320900026 q^{27} - 66648978479332005416 q^{28} - 37318207376924889452 q^{30} - 4 q^{33} + 1458071871715588609864 q^{34} + 401951820620261697956 q^{36} - 4 q^{37} - 15042684037216619346604 q^{39} - 20009156694102269916808 q^{40} + 4441450874324566052856 q^{42} + 14200115812612743847244 q^{43} - 14901161193847656252 q^{45} - 92169885356868519496808 q^{46} - 96141603384608350255440 q^{48} + 3792542056409692739482188 q^{49} - 62120836365748153016328 q^{51} - 119442816650778804368320 q^{52} + 309630658376333184761384 q^{54} + 1516750694338461801016600 q^{55} + 3087997512571516572243896 q^{58} - 993626387815989744483040 q^{60} + 2475467954128860415560428 q^{61} - 10551614275260198405089032 q^{64} + 50930229825606476474116 q^{66} - 16791855426275982771219556 q^{67} + 15251194969972 q^{69} - 13878044235351366512626952 q^{70} - 25426646586961276045942904 q^{72} + 68365696019038351581172334 q^{75} + 141635859808226982924117704 q^{76} - 86406232456843756137762372 q^{78} - 4 q^{81} - 272103516393435008077298112 q^{82} + 124734774854056261061081296 q^{84} + 224109216223749790039062496 q^{85} + 837180858853408838998522884 q^{87} - 616579564401559458769811296 q^{88} + 1243590449430014758833906032 q^{90} + 602184069071493366058474024 q^{91} + 886600140227711910263126236 q^{93} + 135577436448504071900779632 q^{94} + 215572301625623966136226888 q^{96} - 8 q^{97} + 1841950061835766796770917164 q^{99} + O(q^{100})$$

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

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