Properties

Label 112.2.p
Level $112$
Weight $2$
Character orbit 112.p
Rep. character $\chi_{112}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $3$
Sturm bound $32$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 112.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(32\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 44 8 36
Cusp forms 20 8 12
Eisenstein series 24 0 24

Trace form

\( 8q - 4q^{9} + O(q^{10}) \) \( 8q - 4q^{9} + 4q^{21} - 8q^{25} - 24q^{29} - 36q^{33} - 4q^{37} + 36q^{45} + 32q^{49} + 12q^{53} + 56q^{57} + 36q^{61} - 12q^{65} - 12q^{73} - 48q^{77} + 8q^{81} - 72q^{85} - 36q^{89} + 4q^{93} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
112.2.p.a \(2\) \(0.894\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(4\) \(q+(-1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
112.2.p.b \(2\) \(0.894\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(-4\) \(q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
112.2.p.c \(4\) \(0.894\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(-6\) \(0\) \(q+\beta _{1}q^{3}+(-2-\beta _{2})q^{5}-\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

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