↑

Properties

Label 112.2.w
Level $112$
Weight $2$
Character orbit 112.w
Rep. character $\chi_{112}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $56$
Newform subspaces $3$
Sturm bound $32$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 112.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(32\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(112, [\chi])\).

Total New Old
Modular forms 72 72 0
Cusp forms 56 56 0
Eisenstein series 16 16 0

Trace form

\( 56 q - 2 q^{2} - 2 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} - 20 q^{8} + 4 q^{10} - 6 q^{11} - 2 q^{12} - 8 q^{13} - 24 q^{14} - 16 q^{15} + 8 q^{16} - 4 q^{17} + 10 q^{18} - 2 q^{19} + 8 q^{20} - 10 q^{21}+ \cdots + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(112, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
112.2.w.a 112.w 112.w $4$ $0.894$ \(\Q(\zeta_{12})\) None 112.2.w.a \(-2\) \(-4\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}+\cdots)q^{3}+\cdots\)
112.2.w.b 112.w 112.w $4$ $0.894$ \(\Q(\zeta_{12})\) None 112.2.w.a \(4\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
112.2.w.c 112.w 112.w $48$ $0.894$ None 112.2.w.c \(-4\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{12}]$