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Properties

Label 1110.2.bb
Level $1110$
Weight $2$
Character orbit 1110.bb
Rep. character $\chi_{1110}(1009,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $5$
Sturm bound $456$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(456\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1110, [\chi])\).

Total New Old
Modular forms 472 80 392
Cusp forms 440 80 360
Eisenstein series 32 0 32

Trace form

\( 80 q + 40 q^{4} + 40 q^{9} + O(q^{10}) \) \( 80 q + 40 q^{4} + 40 q^{9} + 8 q^{11} + 16 q^{14} - 40 q^{16} - 12 q^{19} - 16 q^{21} - 4 q^{25} - 24 q^{26} - 32 q^{29} - 4 q^{30} - 32 q^{31} + 28 q^{34} - 4 q^{35} + 80 q^{36} + 12 q^{39} + 40 q^{41} + 4 q^{44} - 4 q^{46} + 72 q^{49} + 32 q^{50} + 16 q^{51} + 8 q^{55} + 8 q^{56} - 52 q^{59} + 16 q^{61} - 80 q^{64} + 60 q^{65} + 8 q^{66} + 8 q^{69} - 20 q^{70} - 32 q^{71} - 28 q^{74} + 16 q^{75} + 12 q^{76} - 8 q^{79} - 40 q^{81} - 32 q^{84} + 16 q^{85} - 16 q^{86} + 20 q^{89} + 16 q^{91} - 8 q^{94} - 28 q^{95} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1110, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1110.2.bb.a 1110.bb 185.n $4$ $8.863$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1+\cdots)q^{4}+\cdots\)
1110.2.bb.b 1110.bb 185.n $4$ $8.863$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+\zeta_{12}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1110.2.bb.c 1110.bb 185.n $4$ $8.863$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1+\cdots)q^{4}+\cdots\)
1110.2.bb.d 1110.bb 185.n $28$ $8.863$ None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
1110.2.bb.e 1110.bb 185.n $40$ $8.863$ None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1110, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)