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Properties

Label 112.4.j
Level $112$
Weight $4$
Character orbit 112.j
Rep. character $\chi_{112}(27,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $92$
Newform subspaces $2$
Sturm bound $64$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 112.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(112, [\chi])\).

Total New Old
Modular forms 100 100 0
Cusp forms 92 92 0
Eisenstein series 8 8 0

Trace form

\( 92 q - 4 q^{2} + 6 q^{4} - 4 q^{7} + 80 q^{8} - 24 q^{11} - 122 q^{14} + 146 q^{16} - 202 q^{18} + 52 q^{21} - 390 q^{22} + 320 q^{23} + 96 q^{28} + 196 q^{29} - 552 q^{30} - 984 q^{32} + 476 q^{35} + 32 q^{36}+ \cdots + 3920 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(112, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
112.4.j.a 112.j 112.j $4$ $6.608$ \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) 112.4.j.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(\beta _{1}-3\beta _{3})q^{2}+(-2-5\beta _{2})q^{4}+(-14\beta _{1}+\cdots)q^{7}+\cdots\)
112.4.j.b 112.j 112.j $88$ $6.608$ None 112.4.j.b \(-4\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$