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Properties

Label 44.3.d
Level $44$
Weight $3$
Character orbit 44.d
Rep. character $\chi_{44}(21,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 44 = 2^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 44.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(44, [\chi])\).

Total New Old
Modular forms 15 2 13
Cusp forms 9 2 7
Eisenstein series 6 0 6

Trace form

\( 2 q + 5 q^{3} + q^{5} + 11 q^{9} + O(q^{10}) \) \( 2 q + 5 q^{3} + q^{5} + 11 q^{9} - 22 q^{11} - 47 q^{15} - 35 q^{23} + 99 q^{25} + 65 q^{27} + 37 q^{31} - 55 q^{33} + 25 q^{37} - 242 q^{45} + 100 q^{47} + 98 q^{49} - 140 q^{53} - 11 q^{55} - 107 q^{59} - 35 q^{67} + 61 q^{69} + 133 q^{71} + 198 q^{75} + 212 q^{81} + 97 q^{89} - 155 q^{93} - 95 q^{97} - 121 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(44, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
44.3.d.a 44.d 11.b $2$ $1.199$ \(\Q(\sqrt{33}) \) \(\Q(\sqrt{-11}) \) \(0\) \(5\) \(1\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(3-\beta )q^{3}+(-1+3\beta )q^{5}+(8-5\beta )q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(44, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(44, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)