↑

Properties

Label 55.4.e
Level $55$
Weight $4$
Character orbit 55.e
Rep. character $\chi_{55}(32,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(55, [\chi])\).

Total New Old
Modular forms 40 40 0
Cusp forms 32 32 0
Eisenstein series 8 8 0

Trace form

\( 32 q + 12 q^{5} - 40 q^{11} + 120 q^{12} + 156 q^{15} - 272 q^{16} - 256 q^{20} + 240 q^{22} - 516 q^{25} + 656 q^{26} - 300 q^{27} - 440 q^{31} - 400 q^{33} + 1512 q^{36} - 700 q^{37} - 1120 q^{38} + 1400 q^{42}+ \cdots + 6380 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(55, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
55.4.e.a 55.e 55.e $4$ $3.245$ \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) 55.4.e.a \(0\) \(16\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(4+4\beta _{1}+\beta _{2}+\beta _{3})q^{3}-8\beta _{1}q^{4}+\cdots\)
55.4.e.b 55.e 55.e $28$ $3.245$ None 55.4.e.b \(0\) \(-16\) \(12\) \(0\) $\mathrm{SU}(2)[C_{4}]$