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Properties

Label 73.2.h
Level $73$
Weight $2$
Character orbit 73.h
Rep. character $\chi_{73}(3,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $20$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 73 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 73.h (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 73 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(73, [\chi])\).

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

Trace form

\( 20 q - 4 q^{2} - 8 q^{4} - 4 q^{5} + 6 q^{6} - 2 q^{7} + 12 q^{8} - 32 q^{9} + O(q^{10}) \) \( 20 q - 4 q^{2} - 8 q^{4} - 4 q^{5} + 6 q^{6} - 2 q^{7} + 12 q^{8} - 32 q^{9} - 12 q^{10} - 6 q^{11} + 30 q^{12} - 16 q^{13} - 8 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{18} - 12 q^{19} + 8 q^{20} + 24 q^{21} + 8 q^{22} - 6 q^{23} - 36 q^{25} - 36 q^{26} - 12 q^{28} - 6 q^{29} + 34 q^{30} + 20 q^{31} - 6 q^{32} + 34 q^{33} + 36 q^{34} + 18 q^{35} + 18 q^{36} - 8 q^{37} - 66 q^{38} + 28 q^{39} - 2 q^{40} + 10 q^{41} - 56 q^{42} + 12 q^{43} + 34 q^{44} - 4 q^{45} - 20 q^{47} - 48 q^{48} + 30 q^{50} - 36 q^{51} + 80 q^{52} + 24 q^{53} + 24 q^{54} + 10 q^{55} + 10 q^{57} + 54 q^{58} - 18 q^{59} + 50 q^{60} + 42 q^{61} - 12 q^{62} - 48 q^{63} - 56 q^{64} - 44 q^{65} - 10 q^{66} - 42 q^{67} - 44 q^{68} + 24 q^{69} + 4 q^{71} - 112 q^{72} - 16 q^{73} - 96 q^{74} - 52 q^{75} + 52 q^{77} - 12 q^{78} + 54 q^{79} - 2 q^{80} + 60 q^{81} + 32 q^{82} - 30 q^{83} - 16 q^{84} + 6 q^{85} + 16 q^{86} + 32 q^{87} + 2 q^{88} - 22 q^{89} - 110 q^{90} - 8 q^{91} - 78 q^{92} + 78 q^{93} + 38 q^{94} + 38 q^{95} + 72 q^{96} + 138 q^{98} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(73, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
73.2.h.a 73.h 73.h $20$ $0.583$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-4\) \(0\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{12}]$ \(q-\beta _{9}q^{2}+(\beta _{2}+\beta _{6}-\beta _{8}-\beta _{11}+\beta _{13}+\cdots)q^{3}+\cdots\)