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Properties

Label 44.2.g
Level $44$
Weight $2$
Character orbit 44.g
Rep. character $\chi_{44}(7,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $16$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 44 = 2^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 44.g (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(44, [\chi])\).

Total New Old
Modular forms 32 32 0
Cusp forms 16 16 0
Eisenstein series 16 16 0

Trace form

\( 16 q - 5 q^{2} - q^{4} - 6 q^{5} - 5 q^{6} - 5 q^{8} - 10 q^{9} + O(q^{10}) \) \( 16 q - 5 q^{2} - q^{4} - 6 q^{5} - 5 q^{6} - 5 q^{8} - 10 q^{9} - 22 q^{12} - 10 q^{13} + 8 q^{14} + 23 q^{16} - 10 q^{17} + 20 q^{18} + 16 q^{20} + 17 q^{22} + 25 q^{24} + 6 q^{25} - 4 q^{26} + 20 q^{28} - 10 q^{29} - 12 q^{33} - 6 q^{34} - 30 q^{36} + 18 q^{37} - 38 q^{38} - 40 q^{40} + 10 q^{41} - 26 q^{42} - 28 q^{44} + 40 q^{45} - 30 q^{46} - 36 q^{48} + 6 q^{49} - 15 q^{50} - 10 q^{52} + 38 q^{53} - 12 q^{56} + 30 q^{58} + 52 q^{60} - 10 q^{61} + 70 q^{62} + 23 q^{64} + 36 q^{66} + 60 q^{68} - 16 q^{69} + 12 q^{70} + 45 q^{72} - 30 q^{73} + 40 q^{74} + 2 q^{77} + 4 q^{78} - 28 q^{80} - 4 q^{81} - 59 q^{82} - 10 q^{84} - 50 q^{85} - 39 q^{86} - 53 q^{88} - 36 q^{89} - 50 q^{90} + 36 q^{92} - 38 q^{93} - 30 q^{94} - 68 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(44, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
44.2.g.a 44.g 44.g $16$ $0.351$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-5\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{1}-\beta _{2}-\beta _{13}-\beta _{14}+\cdots)q^{3}+\cdots\)