Properties

Label 2112.2.q
Level $2112$
Weight $2$
Character orbit 2112.q
Rep. character $\chi_{2112}(175,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $1$
Sturm bound $768$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2112 = 2^{6} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2112.q (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 176 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(768\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2112, [\chi])\).

Total New Old
Modular forms 800 96 704
Cusp forms 736 96 640
Eisenstein series 64 0 64

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 8 q^{11} - 32 q^{23} + 32 q^{37} - 96 q^{49} - 32 q^{53} - 32 q^{55} - 32 q^{59} + 16 q^{67} - 64 q^{71} + 32 q^{75} + 16 q^{77} - 96 q^{81} + 16 q^{91} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2112, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2112.2.q.a 2112.q 176.i $96$ $16.864$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2112, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2112, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(704, [\chi])\)\(^{\oplus 2}\)