↑

Properties

Label 1116.2.p
Level $1116$
Weight $2$
Character orbit 1116.p
Rep. character $\chi_{1116}(533,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $1$
Sturm bound $384$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1116 = 2^{2} \cdot 3^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1116.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 279 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(384\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 396 64 332
Cusp forms 372 64 308
Eisenstein series 24 0 24

Trace form

\( 64 q + 2 q^{7} + 2 q^{9} + O(q^{10}) \) \( 64 q + 2 q^{7} + 2 q^{9} + 6 q^{15} - 2 q^{19} - 12 q^{21} - 9 q^{23} - 70 q^{25} - 27 q^{27} - q^{31} - 9 q^{37} + 4 q^{39} + 4 q^{45} - 21 q^{47} + 66 q^{49} + 10 q^{51} - 6 q^{53} + 27 q^{55} - 30 q^{57} + 3 q^{59} - 21 q^{61} - 16 q^{63} + 6 q^{65} - 8 q^{67} + 37 q^{69} + 39 q^{71} + 21 q^{73} - 78 q^{75} + 42 q^{81} + 12 q^{83} - 7 q^{87} - 36 q^{89} + 5 q^{93} + 90 q^{95} - 4 q^{97} - 39 q^{99} + O(q^{100}) \)

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.p.a 1116.p 279.o $64$ $8.911$ None 1116.2.p.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(1116, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(279, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(558, [\chi])\)\(^{\oplus 2}\)