Properties

Label 55.2.e
Level $55$
Weight $2$
Character orbit 55.e
Rep. character $\chi_{55}(32,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
Newform subspaces $2$
Sturm bound $12$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 55.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(55, [\chi])\).

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

Trace form

\( 8 q - 6 q^{3} - 8 q^{5} + O(q^{10}) \) \( 8 q - 6 q^{3} - 8 q^{5} + 4 q^{11} + 8 q^{12} - 4 q^{15} - 12 q^{16} + 24 q^{20} - 20 q^{22} + 14 q^{23} + 14 q^{25} - 40 q^{26} + 6 q^{27} + 8 q^{31} - 26 q^{33} + 36 q^{36} - 2 q^{37} + 40 q^{38} - 22 q^{45} - 12 q^{47} + 4 q^{48} - 16 q^{53} + 14 q^{55} - 40 q^{58} - 64 q^{60} + 40 q^{66} + 38 q^{67} - 44 q^{71} + 36 q^{75} + 40 q^{78} - 8 q^{80} + 12 q^{81} + 40 q^{82} - 20 q^{88} + 48 q^{92} + 58 q^{93} - 62 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(55, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
55.2.e.a 55.e 55.e $4$ $0.439$ \(\Q(i, \sqrt{10})\) None 55.2.e.a \(0\) \(-4\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+3\beta _{2}q^{4}+\cdots\)
55.2.e.b 55.e 55.e $4$ $0.439$ \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) 55.2.e.b \(0\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+\beta _{1}-\beta _{3})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)