Properties

Label 1110.2.ba
Level $1110$
Weight $2$
Character orbit 1110.ba
Rep. character $\chi_{1110}(529,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $2$
Sturm bound $456$
Trace bound $2$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 472 72 400
Cusp forms 440 72 368
Eisenstein series 32 0 32

Trace form

\( 72q - 36q^{4} + 6q^{5} + 36q^{9} + O(q^{10}) \) \( 72q - 36q^{4} + 6q^{5} + 36q^{9} + 4q^{10} + 8q^{11} - 36q^{16} + 12q^{19} - 6q^{20} + 2q^{25} + 56q^{26} - 4q^{30} - 60q^{35} - 72q^{36} + 12q^{39} - 2q^{40} + 20q^{41} - 4q^{44} + 20q^{46} + 20q^{49} - 6q^{50} + 96q^{55} + 36q^{59} - 12q^{61} + 72q^{64} + 8q^{65} + 24q^{69} - 20q^{70} - 48q^{71} - 68q^{74} + 16q^{75} - 12q^{76} - 36q^{81} + 52q^{85} + 2q^{90} - 72q^{91} + 24q^{94} - 12q^{95} + 4q^{99} + O(q^{100}) \)

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.ba.a \(36\) \(8.863\) None \(-18\) \(0\) \(2\) \(0\)
1110.2.ba.b \(36\) \(8.863\) None \(18\) \(0\) \(4\) \(0\)

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

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