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Properties

Label 112.3.s
Level $112$
Weight $3$
Character orbit 112.s
Rep. character $\chi_{112}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $14$
Newform subspaces $3$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 112.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(1\)
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 18 58
Cusp forms 52 14 38
Eisenstein series 24 4 20

Trace form

\( 14 q + 3 q^{3} - 3 q^{5} + 10 q^{7} + 14 q^{9} + O(q^{10}) \) \( 14 q + 3 q^{3} - 3 q^{5} + 10 q^{7} + 14 q^{9} - 7 q^{11} + 22 q^{15} - 3 q^{17} + 51 q^{19} - 19 q^{21} + 9 q^{23} + 6 q^{25} - 68 q^{29} - 93 q^{31} + 69 q^{33} - 93 q^{35} - 25 q^{37} + 16 q^{39} - 172 q^{43} - 150 q^{45} - 141 q^{47} - 2 q^{49} + 75 q^{51} - 49 q^{53} + 58 q^{57} + 99 q^{59} + 69 q^{61} + 98 q^{63} + 112 q^{65} + 65 q^{67} + 484 q^{71} + 117 q^{73} + 510 q^{75} - 9 q^{77} - 23 q^{79} + 105 q^{81} - 22 q^{85} - 186 q^{87} - 75 q^{89} - 144 q^{91} + 109 q^{93} - 213 q^{95} - 1052 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.s.a 112.s 7.d $2$ $3.052$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(3\) \(14\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+7q^{7}+\cdots\)
112.3.s.b 112.s 7.d $4$ $3.052$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(6\) \(-6\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2+\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
112.3.s.c 112.s 7.d $8$ $3.052$ 8.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{3}-\beta _{7}q^{5}+(2-3\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(112, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)