Properties

Label 1110.2.o
Level $1110$
Weight $2$
Character orbit 1110.o
Rep. character $\chi_{1110}(253,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $76$
Newform subspaces $2$
Sturm bound $456$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.o (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

\( 76q + 4q^{2} + 76q^{4} + 4q^{5} + 4q^{8} + O(q^{10}) \) \( 76q + 4q^{2} + 76q^{4} + 4q^{5} + 4q^{8} - 4q^{10} - 8q^{14} + 76q^{16} - 8q^{19} + 4q^{20} - 4q^{25} + 16q^{26} - 36q^{29} + 24q^{31} + 4q^{32} + 40q^{35} + 36q^{37} - 8q^{39} - 4q^{40} - 32q^{43} - 12q^{50} + 16q^{51} + 12q^{53} - 16q^{55} - 8q^{56} - 16q^{57} + 36q^{58} + 8q^{59} - 12q^{61} + 32q^{62} + 76q^{64} - 48q^{65} - 8q^{66} - 32q^{67} + 16q^{69} - 16q^{70} + 32q^{71} - 4q^{73} - 20q^{74} + 32q^{75} - 8q^{76} + 16q^{77} + 24q^{79} + 4q^{80} - 76q^{81} + 32q^{86} + 12q^{89} + 32q^{91} - 16q^{93} - 32q^{94} + 48q^{95} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1110.2.o.a \(36\) \(8.863\) None \(-36\) \(0\) \(4\) \(4\)
1110.2.o.b \(40\) \(8.863\) None \(40\) \(0\) \(0\) \(-4\)

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

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