↑

Properties

Label 296.2.j
Level $296$
Weight $2$
Character orbit 296.j
Rep. character $\chi_{296}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
Newform subspaces $2$
Sturm bound $76$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 296 = 2^{3} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 296.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 296 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(76\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(296, [\chi])\).

Total New Old
Modular forms 80 80 0
Cusp forms 72 72 0
Eisenstein series 8 8 0

Trace form

\( 72 q - 4 q^{2} + 2 q^{6} - 4 q^{8} - 72 q^{9} - 4 q^{10} + 8 q^{12} + 10 q^{14} - 24 q^{16} - 8 q^{17} + 14 q^{18} - 4 q^{19} + 4 q^{20} + 14 q^{22} + 44 q^{24} - 4 q^{26} - 4 q^{32} + 16 q^{33} - 20 q^{34}+ \cdots + 78 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(296, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
296.2.j.a 296.j 296.j $8$ $2.364$ 8.0.\(\cdots\).12 None 296.2.j.a \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{2})q^{2}+(-\beta _{2}-\beta _{6})q^{3}-2\beta _{2}q^{4}+\cdots\)
296.2.j.b 296.j 296.j $64$ $2.364$ None 296.2.j.b \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$