Properties

Label 112.7.s
Level $112$
Weight $7$
Character orbit 112.s
Rep. character $\chi_{112}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $46$
Newform subspaces $5$
Sturm bound $112$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 112.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(112\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(112, [\chi])\).

Total New Old
Modular forms 204 50 154
Cusp forms 180 46 134
Eisenstein series 24 4 20

Trace form

\( 46 q + 3 q^{3} - 3 q^{5} - 358 q^{7} + 5102 q^{9} + O(q^{10}) \) \( 46 q + 3 q^{3} - 3 q^{5} - 358 q^{7} + 5102 q^{9} + 681 q^{11} + 1462 q^{15} - 3 q^{17} + 15123 q^{19} - 8755 q^{21} + 12185 q^{23} + 47446 q^{25} - 16068 q^{29} - 110877 q^{31} - 13611 q^{33} + 89187 q^{35} - 1801 q^{37} + 42736 q^{39} + 102004 q^{43} + 228810 q^{45} + 188499 q^{47} - 113666 q^{49} - 301413 q^{51} + 50159 q^{53} + 417850 q^{57} + 664611 q^{59} + 264597 q^{61} + 798434 q^{63} + 103952 q^{65} - 360767 q^{67} - 808028 q^{71} - 385563 q^{73} + 811950 q^{75} - 770393 q^{77} + 572089 q^{79} - 955143 q^{81} + 619338 q^{85} - 3755130 q^{87} - 881499 q^{89} - 3439920 q^{91} + 563149 q^{93} + 2991867 q^{95} + 714148 q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(112, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
112.7.s.a $2$ $25.766$ \(\Q(\sqrt{-3}) \) None \(0\) \(21\) \(315\) \(686\) \(q+(7+7\zeta_{6})q^{3}+(210-105\zeta_{6})q^{5}+\cdots\)
112.7.s.b $4$ $25.766$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-18\) \(-150\) \(-280\) \(q+(-6-3\beta _{1}-13\beta _{3})q^{3}+(-5^{2}+5^{2}\beta _{1}+\cdots)q^{5}+\cdots\)
112.7.s.c $8$ $25.766$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-336\) \(-652\) \(q+(\beta _{3}+\beta _{7})q^{3}+(-56+28\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
112.7.s.d $8$ $25.766$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(168\) \(452\) \(q-\beta _{3}q^{3}+(28-14\beta _{1}-\beta _{5})q^{5}+(11^{2}+\cdots)q^{7}+\cdots\)
112.7.s.e $24$ $25.766$ None \(0\) \(0\) \(0\) \(-564\)

Decomposition of \(S_{7}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(112, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)