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Properties

Label 1116.2.m
Level $1116$
Weight $2$
Character orbit 1116.m
Rep. character $\chi_{1116}(109,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $56$
Newform subspaces $7$
Sturm bound $384$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1116 = 2^{2} \cdot 3^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1116.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 7 \)
Sturm bound: \(384\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1116, [\chi])\).

Total New Old
Modular forms 816 56 760
Cusp forms 720 56 664
Eisenstein series 96 0 96

Trace form

\( 56 q - 2 q^{5} - 4 q^{7} + O(q^{10}) \) \( 56 q - 2 q^{5} - 4 q^{7} - q^{11} - 3 q^{13} + 12 q^{17} - 2 q^{19} - 6 q^{23} + 94 q^{25} + 9 q^{31} + 8 q^{35} - 8 q^{37} - 17 q^{41} + 10 q^{43} - 6 q^{47} - 26 q^{49} + 28 q^{53} + 8 q^{55} + 22 q^{59} + 48 q^{61} + 47 q^{65} + 44 q^{67} + 40 q^{73} + 31 q^{77} - 37 q^{79} + 5 q^{83} - 20 q^{85} + 10 q^{89} + 3 q^{91} + 47 q^{95} + 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1116, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1116.2.m.a 1116.m 31.d $4$ $8.911$ \(\Q(\zeta_{10})\) None 124.2.f.a \(0\) \(0\) \(-8\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q-2q^{5}+(\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{7}+\cdots\)
1116.2.m.b 1116.m 31.d $4$ $8.911$ \(\Q(\zeta_{10})\) None 372.2.j.a \(0\) \(0\) \(4\) \(6\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{5}+(3\zeta_{10}+\cdots)q^{7}+\cdots\)
1116.2.m.c 1116.m 31.d $4$ $8.911$ \(\Q(\zeta_{10})\) None 124.2.f.b \(0\) \(0\) \(6\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}^{2}+\zeta_{10}^{3})q^{5}+(2\zeta_{10}-3\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
1116.2.m.d 1116.m 31.d $8$ $8.911$ 8.0.1903140625.1 None 372.2.j.b \(0\) \(0\) \(-2\) \(-9\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{2}+\beta _{4}+\beta _{6})q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
1116.2.m.e 1116.m 31.d $8$ $8.911$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-3}) \) 1116.2.m.e \(0\) \(0\) \(0\) \(8\) $\mathrm{U}(1)[D_{5}]$ \(q+(2+2\zeta_{15}+2\zeta_{15}^{2}+\zeta_{15}^{6}+\zeta_{15}^{7})q^{7}+\cdots\)
1116.2.m.f 1116.m 31.d $12$ $8.911$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 372.2.j.c \(0\) \(0\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{3}q^{5}+(\beta _{2}-\beta _{6}-\beta _{7})q^{7}+(-\beta _{4}+\cdots)q^{11}+\cdots\)
1116.2.m.g 1116.m 31.d $16$ $8.911$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 1116.2.m.g \(0\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}-\beta _{3}-\beta _{6}-\beta _{10})q^{5}+(-2+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1116, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1116, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(124, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(279, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(372, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(558, [\chi])\)\(^{\oplus 2}\)