# Properties

 Label 23.31.b Level $23$ Weight $31$ Character orbit 23.b Rep. character $\chi_{23}(22,\cdot)$ Character field $\Q$ Dimension $59$ Newform subspaces $3$ Sturm bound $62$ Trace bound $1$

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## Defining parameters

 Level: $$N$$ $$=$$ $$23$$ Weight: $$k$$ $$=$$ $$31$$ 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: $$62$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{31}(23, [\chi])$$.

Total New Old
Modular forms 61 61 0
Cusp forms 59 59 0
Eisenstein series 2 2 0

## Trace form

 $$59 q - 48952 q^{2} + 10327710 q^{3} + 33767800104 q^{4} - 749726814525 q^{6} - 61701776229125 q^{8} + 3710634725393769 q^{9} + O(q^{10})$$ $$59 q - 48952 q^{2} + 10327710 q^{3} + 33767800104 q^{4} - 749726814525 q^{6} - 61701776229125 q^{8} + 3710634725393769 q^{9} + 6137116703764203 q^{12} + 58617078084326254 q^{13} + 21886842705983044624 q^{16} - 20909733962985256341 q^{18} - 92000548241212598117 q^{23} - 1209423960683522072400 q^{24} - 10961057055780336892645 q^{25} + 2808127993053766005955 q^{26} - 3659895230794846654236 q^{27} - 31696256077143021470602 q^{29} - 86187690941416624136042 q^{31} - 34975559163035828475072 q^{32} - 143774039466185247067560 q^{35} + 1788968268273175351018419 q^{36} - 3581108647370152369341900 q^{39} + 3450235315277395543325078 q^{41} - 45483188907564462438419360 q^{46} + 2247253369881005972240582 q^{47} + 98498743870258303999111323 q^{48} - 207187415599804090439803213 q^{49} + 286376616167955534408567320 q^{50} + 102176788008668071706594307 q^{52} - 195960694440434093422499925 q^{54} + 114096042481291566296702520 q^{55} + 387383964698044021776724379 q^{58} - 950127090162227864082982642 q^{59} - 2473704971992461046293863597 q^{62} + 18849324334255651116873406739 q^{64} + 857719036012131936040114950 q^{69} - 3218856207872588007686905920 q^{70} + 13497708300802255639803693278 q^{71} + 1435053582014687317457598627 q^{72} + 6342542769935152043759142574 q^{73} - 38021078600273057821548807930 q^{75} + 135322459371608693646635563032 q^{77} + 290885795972155587588179865651 q^{78} + 116225255831199434229617263359 q^{81} - 1280965946478967863161912245 q^{82} - 287295896244371821694585243160 q^{85} + 171675186991175760954737685084 q^{87} + 240259129917236372834353006248 q^{92} + 2263262550390667374137409993036 q^{93} + 2355525655971903398658963325115 q^{94} + 422004400436441552339349905520 q^{95} - 2278759307964494995138413933525 q^{96} + 2797210593318328617237444105176 q^{98} + O(q^{100})$$

## Decomposition of $$S_{31}^{\mathrm{new}}(23, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
23.31.b.a $1$ $131.133$ $$\Q$$ $$\Q(\sqrt{-23})$$ $$-50407$$ $$19799482$$ $$0$$ $$0$$ $$q-50407q^{2}+19799482q^{3}+1467123825q^{4}+\cdots$$
23.31.b.b $2$ $131.133$ $$\Q(\sqrt{69})$$ $$\Q(\sqrt{-23})$$ $$50407$$ $$-19799482$$ $$0$$ $$0$$ $$q+(29570-8733\beta )q^{2}+(-12065545+\cdots)q^{3}+\cdots$$
23.31.b.c $56$ $131.133$ None $$-48952$$ $$10327710$$ $$0$$ $$0$$