Properties

Label 25.6.e
Level $25$
Weight $6$
Character orbit 25.e
Rep. character $\chi_{25}(4,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $48$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 25.e (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(25, [\chi])\).

Total New Old
Modular forms 56 56 0
Cusp forms 48 48 0
Eisenstein series 8 8 0

Trace form

\( 48q - 5q^{2} - 5q^{3} + 189q^{4} - 60q^{5} - 139q^{6} + 610q^{8} + 1031q^{9} + O(q^{10}) \) \( 48q - 5q^{2} - 5q^{3} + 189q^{4} - 60q^{5} - 139q^{6} + 610q^{8} + 1031q^{9} + 435q^{10} - 724q^{11} + 315q^{12} - 5q^{13} - 497q^{14} - 105q^{15} - 6967q^{16} - 960q^{17} + 4075q^{19} + 9155q^{20} + 2016q^{21} - 5450q^{22} - 10995q^{23} - 20720q^{24} - 16610q^{25} + 21666q^{26} - 13805q^{27} + 14235q^{28} + 17195q^{29} + 39595q^{30} + 8631q^{31} + 28460q^{33} - 24067q^{34} - 4145q^{35} - 43827q^{36} + 19980q^{37} - 77385q^{38} + 6037q^{39} + 93210q^{40} - 26514q^{41} + 182885q^{42} + 26748q^{44} - 94185q^{45} - 14559q^{46} - 7700q^{47} - 127830q^{48} - 130126q^{49} - 231115q^{50} + 121116q^{51} - 189260q^{52} + 45840q^{53} + 19985q^{54} + 79370q^{55} - 43280q^{56} + 337370q^{58} + 47640q^{59} + 71480q^{60} + 7791q^{61} + 135320q^{62} - 35790q^{63} + 68204q^{64} + 197485q^{65} - 14798q^{66} - 66180q^{67} + 17957q^{69} - 129930q^{70} - 46694q^{71} - 50545q^{72} - 18985q^{73} - 183292q^{74} - 202210q^{75} + 273360q^{76} - 132990q^{77} - 665225q^{78} - 54065q^{79} + 362810q^{80} - 382452q^{81} + 161155q^{83} + 474258q^{84} - 83075q^{85} + 74691q^{86} + 897680q^{87} + 578430q^{88} + 436475q^{89} + 775655q^{90} + 181046q^{91} - 1412870q^{92} - 336327q^{94} - 362785q^{95} - 766024q^{96} - 475210q^{97} - 361660q^{98} - 451848q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
25.6.e.a \(48\) \(4.010\) None \(-5\) \(-5\) \(-60\) \(0\)