Properties

Label 44.2.c
Level $44$
Weight $2$
Character orbit 44.c
Rep. character $\chi_{44}(43,\cdot)$
Character field $\Q$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q\)
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 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\( 4 q - 4 q^{4} - 4 q^{5} + O(q^{10}) \) \( 4 q - 4 q^{4} - 4 q^{5} + 12 q^{12} - 8 q^{14} - 8 q^{16} + 4 q^{20} + 8 q^{22} - 16 q^{25} + 24 q^{26} + 12 q^{33} - 24 q^{34} + 12 q^{37} + 8 q^{38} - 24 q^{42} - 12 q^{44} - 24 q^{48} + 4 q^{49} - 8 q^{53} + 32 q^{56} - 12 q^{60} + 32 q^{64} + 24 q^{66} + 36 q^{69} + 8 q^{70} - 32 q^{77} - 24 q^{78} + 8 q^{80} - 36 q^{81} + 24 q^{82} - 16 q^{86} - 32 q^{88} - 4 q^{89} - 36 q^{92} - 12 q^{93} + 28 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
44.2.c.a 44.c 44.c $4$ $0.351$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 44.2.c.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots\)