Properties

Label 112.2.i
Level $112$
Weight $2$
Character orbit 112.i
Rep. character $\chi_{112}(65,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $6$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
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 10 34
Cusp forms 20 6 14
Eisenstein series 24 4 20

Trace form

\( 6 q + 3 q^{3} - q^{5} + 4 q^{7} - 2 q^{9} + O(q^{10}) \) \( 6 q + 3 q^{3} - q^{5} + 4 q^{7} - 2 q^{9} - q^{11} - 4 q^{13} - 2 q^{15} - q^{17} + 5 q^{19} - 3 q^{21} - 7 q^{23} + 4 q^{25} - 18 q^{27} - 20 q^{29} - 13 q^{31} + 9 q^{33} - 21 q^{35} + 3 q^{37} + 14 q^{39} - 12 q^{41} + 24 q^{43} + 10 q^{45} - 3 q^{47} + 6 q^{49} + 17 q^{51} + 7 q^{53} + 22 q^{55} + 26 q^{57} + 27 q^{59} + 3 q^{61} + 38 q^{63} - 10 q^{65} - 5 q^{67} + 2 q^{69} - 32 q^{71} - 13 q^{73} - 4 q^{75} + 17 q^{77} - 23 q^{79} - 11 q^{81} - 40 q^{83} + 22 q^{85} - 26 q^{87} - 13 q^{89} - 24 q^{91} + 5 q^{93} - 9 q^{95} - 12 q^{97} + 12 q^{99} + O(q^{100}) \)

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.i.a $2$ $0.894$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(4\) \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
112.2.i.b $2$ $0.894$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-3\) \(4\) \(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
112.2.i.c $2$ $0.894$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(1\) \(-4\) \(q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)

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

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