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Properties

Label 25.2.d
Level $25$
Weight $2$
Character orbit 25.d
Rep. character $\chi_{25}(6,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $4$
Newform subspaces $1$
Sturm bound $5$
Trace bound $0$

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(25, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

Trace form

\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} - q^{3} - 2 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9} + 10 q^{10} - 2 q^{11} + 3 q^{12} + 9 q^{13} + q^{14} - 5 q^{15} - 6 q^{16} + 8 q^{17} + 4 q^{18} - 5 q^{19} + 5 q^{20} - 2 q^{21} - 14 q^{22} - 11 q^{23} - 5 q^{25} - 12 q^{26} + 5 q^{27} + q^{28} + 5 q^{29} - 5 q^{30} + 3 q^{31} + 18 q^{32} + 8 q^{33} + 6 q^{34} + 5 q^{35} - 6 q^{36} - 7 q^{37} + 5 q^{38} + 9 q^{39} + 5 q^{40} + 8 q^{41} + q^{42} - 6 q^{43} + 6 q^{44} - 10 q^{45} + 13 q^{46} - 2 q^{47} - 6 q^{48} - 22 q^{49} - 10 q^{50} - 12 q^{51} - 12 q^{52} + 9 q^{53} - 15 q^{54} + 20 q^{55} - 10 q^{57} - 10 q^{58} + 13 q^{61} + 6 q^{62} - 6 q^{63} + 3 q^{64} + 6 q^{66} - 2 q^{67} - 4 q^{68} - q^{69} + 8 q^{71} + 10 q^{72} + 9 q^{73} + 6 q^{74} + 20 q^{75} + 20 q^{76} - 4 q^{77} + 3 q^{78} + 15 q^{79} - 15 q^{80} - q^{81} - 4 q^{82} + 9 q^{83} - 4 q^{84} - 20 q^{85} + 3 q^{86} - 10 q^{88} - 20 q^{89} - 12 q^{91} - 12 q^{92} - 12 q^{93} + q^{94} - 5 q^{95} - 2 q^{96} + 8 q^{97} + 11 q^{98} + 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
25.2.d.a 25.d 25.d $4$ $0.200$ \(\Q(\zeta_{10})\) None \(-2\) \(-1\) \(-5\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)