# Properties

 Label 23.25.b Level $23$ Weight $25$ Character orbit 23.b Rep. character $\chi_{23}(22,\cdot)$ Character field $\Q$ Dimension $47$ Newform subspaces $3$ Sturm bound $50$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$23$$ Weight: $$k$$ $$=$$ $$25$$ Character orbit: $$[\chi]$$ $$=$$ 23.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$23$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$50$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{25}(23, [\chi])$$.

Total New Old
Modular forms 49 49 0
Cusp forms 47 47 0
Eisenstein series 2 2 0

## Trace form

 $$47 q - 4232 q^{2} - 434562 q^{3} + 368092008 q^{4} - 5593673229 q^{6} + 74005246931 q^{8} + 5067330597741 q^{9} + O(q^{10})$$ $$47 q - 4232 q^{2} - 434562 q^{3} + 368092008 q^{4} - 5593673229 q^{6} + 74005246931 q^{8} + 5067330597741 q^{9} - 20495626037781 q^{12} + 5771152551358 q^{13} + 2645975722662160 q^{16} - 67874545343901 q^{18} - 51460339967149681 q^{23} - 138403526810384928 q^{24} - 510719149831430737 q^{25} - 156378094452632245 q^{26} - 75036056343782244 q^{27} - 1583078054945709602 q^{29} - 77249813729122274 q^{31} + 1729924952099667744 q^{32} + 3418569899175948192 q^{35} + 59704767230759576787 q^{36} + 5479950003975867036 q^{39} - 9150679195666184738 q^{41} - 153049487518536134480 q^{46} + 22735751396127769438 q^{47} - 1057301601893947741005 q^{48} - 1267367077864783003633 q^{49} + 284936617115007894520 q^{50} - 14496567845913196581 q^{52} + 427769653530153047427 q^{54} - 5430040696094013021792 q^{55} - 3667715980251537830869 q^{58} + 6557824862401315128190 q^{59} + 22074091739305233447011 q^{62} + 30861270600445749976931 q^{64} + 24476879859710435470878 q^{69} - 118028399895318845638416 q^{70} - 68204988047209908888578 q^{71} - 61925219427170615767677 q^{72} - 7319375899831086678722 q^{73} + 12913295383070041819998 q^{75} + 111116199573084838704480 q^{77} - 133352085616887279140973 q^{78} - 92050958955139484028597 q^{81} + 446732006608621898235851 q^{82} - 113385735487939722862944 q^{85} + 792703860282786755228796 q^{87} - 3135455949007530391355688 q^{92} + 2490474357216657706818876 q^{93} - 607510120409074977795901 q^{94} - 1668692394291208047471936 q^{95} - 7831523450234609872700637 q^{96} - 2067304853876486831513192 q^{98} + O(q^{100})$$

## Decomposition of $$S_{25}^{\mathrm{new}}(23, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
23.25.b.a $1$ $83.942$ $$\Q$$ $$\Q(\sqrt{-23})$$ $$-1951$$ $$-1062686$$ $$0$$ $$0$$ $$q-1951q^{2}-1062686q^{3}-12970815q^{4}+\cdots$$
23.25.b.b $2$ $83.942$ $$\Q(\sqrt{69})$$ $$\Q(\sqrt{-23})$$ $$1951$$ $$1062686$$ $$0$$ $$0$$ $$q+(1094+237\beta )q^{2}+(531039-608\beta )q^{3}+\cdots$$
23.25.b.c $44$ $83.942$ None $$-4232$$ $$-434562$$ $$0$$ $$0$$