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Properties

Label 44.2.e
Level $44$
Weight $2$
Character orbit 44.e
Rep. character $\chi_{44}(5,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $4$
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.e (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
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 36 4 32
Cusp forms 12 4 8
Eisenstein series 24 0 24

Trace form

\( 4 q - q^{3} + 3 q^{5} - 7 q^{7} - 8 q^{9} + O(q^{10}) \) \( 4 q - q^{3} + 3 q^{5} - 7 q^{7} - 8 q^{9} - 4 q^{11} - q^{13} + 3 q^{15} - q^{17} + 7 q^{19} + 18 q^{21} + 8 q^{23} + 6 q^{25} + 5 q^{27} - 5 q^{29} - 5 q^{31} - 19 q^{33} - 9 q^{35} - 9 q^{37} + 9 q^{39} - 5 q^{41} - 16 q^{45} - 5 q^{47} - 12 q^{49} - q^{51} + 11 q^{53} + 7 q^{55} + 17 q^{57} + 17 q^{59} - q^{61} + 4 q^{63} - 2 q^{65} + 16 q^{67} + 8 q^{69} + 5 q^{71} + 19 q^{73} - 9 q^{75} + 37 q^{77} + 3 q^{79} - 16 q^{81} - 31 q^{83} - 7 q^{85} - 50 q^{87} - 16 q^{89} - 27 q^{91} + 5 q^{93} - q^{95} + 27 q^{97} + 8 q^{99} + O(q^{100}) \)

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.e.a 44.e 11.c $4$ $0.351$ \(\Q(\zeta_{10})\) None \(0\) \(-1\) \(3\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}+2\zeta_{10}^{3})q^{3}+(1-\zeta_{10}^{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(44, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(44, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)