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Properties

Label 61.2.e
Level $61$
Weight $2$
Character orbit 61.e
Rep. character $\chi_{61}(9,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $12$
Newform subspaces $1$
Sturm bound $10$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 61.e (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 61 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(61, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

Trace form

\( 12 q - 2 q^{2} - q^{3} + 2 q^{4} - 5 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} - 6 q^{9} + O(q^{10}) \) \( 12 q - 2 q^{2} - q^{3} + 2 q^{4} - 5 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} - 6 q^{9} - 6 q^{10} - 6 q^{11} + 6 q^{12} + 2 q^{13} - 2 q^{14} - 5 q^{15} + 10 q^{16} + 6 q^{17} - 15 q^{18} - q^{19} + 13 q^{20} + 32 q^{21} - 25 q^{22} - 7 q^{23} - 12 q^{25} + 2 q^{26} + 8 q^{27} - 13 q^{28} - 8 q^{29} + 3 q^{30} + 19 q^{31} + 26 q^{32} - q^{33} - 30 q^{34} + 10 q^{35} + 8 q^{36} + 31 q^{37} + 27 q^{38} - 23 q^{39} + 4 q^{41} + 11 q^{42} + q^{43} - 20 q^{44} - 18 q^{45} + 23 q^{46} - 22 q^{47} - 8 q^{48} + 3 q^{49} + 74 q^{50} + 9 q^{52} - 35 q^{53} - 26 q^{54} - 18 q^{56} - 31 q^{57} - 16 q^{58} - 13 q^{59} + 2 q^{60} - 6 q^{61} - 52 q^{62} + 7 q^{63} + 16 q^{64} + 4 q^{65} - 19 q^{66} - 9 q^{67} - 33 q^{68} + 35 q^{69} - 5 q^{70} - 24 q^{71} - 30 q^{72} + 51 q^{73} - 20 q^{74} + 40 q^{75} - 31 q^{76} + q^{77} + 22 q^{78} - 26 q^{79} - 23 q^{80} - 2 q^{81} + 78 q^{82} + 3 q^{83} + 17 q^{84} + 18 q^{85} + 55 q^{86} + 49 q^{87} - q^{88} - 17 q^{89} + 54 q^{90} - 27 q^{91} + 37 q^{92} + 10 q^{93} + 13 q^{94} + 4 q^{95} - 17 q^{96} + 17 q^{97} + 29 q^{98} + 19 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(61, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
61.2.e.a 61.e 61.e $12$ $0.487$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(-1\) \(-5\) \(-10\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{5}q^{2}+(\beta _{8}+\beta _{10})q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)