Properties

Label 112.3.r
Level $112$
Weight $3$
Character orbit 112.r
Rep. character $\chi_{112}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $3$
Sturm bound $48$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 112.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(112, [\chi])\).

Total New Old
Modular forms 76 16 60
Cusp forms 52 16 36
Eisenstein series 24 0 24

Trace form

\( 16 q + 24 q^{9} + O(q^{10}) \) \( 16 q + 24 q^{9} + 16 q^{13} + 72 q^{21} - 16 q^{25} - 144 q^{29} - 72 q^{33} - 40 q^{37} - 48 q^{41} - 120 q^{45} - 272 q^{49} - 24 q^{53} + 144 q^{57} - 40 q^{61} + 264 q^{65} + 768 q^{69} + 376 q^{73} + 432 q^{77} - 288 q^{81} - 240 q^{85} + 264 q^{89} - 456 q^{93} - 272 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(112, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
112.3.r.a 112.r 28.g $4$ $3.052$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(3\beta _{1}-\beta _{3})q^{7}-2\beta _{2}q^{9}+\cdots\)
112.3.r.b 112.r 28.g $6$ $3.052$ 6.0.259470000.1 None \(0\) \(-3\) \(-1\) \(-14\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{5})q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
112.3.r.c 112.r 28.g $6$ $3.052$ 6.0.259470000.1 None \(0\) \(3\) \(-1\) \(14\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{5})q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(112, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)