↑

Properties

Label 1110.2.l
Level $1110$
Weight $2$
Character orbit 1110.l
Rep. character $\chi_{1110}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $76$
Newform subspaces $2$
Sturm bound $456$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(456\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 472 76 396
Cusp forms 440 76 364
Eisenstein series 32 0 32

Trace form

\( 76 q - 76 q^{4} + O(q^{10}) \) \( 76 q - 76 q^{4} - 4 q^{10} + 8 q^{14} + 76 q^{16} - 8 q^{17} - 4 q^{18} + 8 q^{19} + 16 q^{22} + 4 q^{25} + 16 q^{26} + 36 q^{29} + 24 q^{31} + 8 q^{35} + 16 q^{37} + 8 q^{39} + 4 q^{40} + 4 q^{45} - 16 q^{50} + 16 q^{51} + 12 q^{53} + 32 q^{55} - 8 q^{56} - 36 q^{58} - 8 q^{59} - 12 q^{61} - 32 q^{62} - 76 q^{64} + 48 q^{65} - 8 q^{66} + 32 q^{67} + 8 q^{68} - 16 q^{69} - 16 q^{70} + 32 q^{71} + 4 q^{72} + 4 q^{73} + 20 q^{74} + 32 q^{75} - 8 q^{76} - 16 q^{77} - 24 q^{79} - 76 q^{81} - 32 q^{82} + 32 q^{86} - 16 q^{88} - 12 q^{89} + 32 q^{91} + 32 q^{94} - 48 q^{95} + 80 q^{97} - 68 q^{98} + O(q^{100}) \)

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.l.a 1110.l 185.f $36$ $8.863$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$
1110.2.l.b 1110.l 185.f $40$ $8.863$ None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)