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

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

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.bb.a \(4\) \(8.863\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1+\cdots)q^{4}+\cdots\)
1110.2.bb.b \(4\) \(8.863\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+\zeta_{12}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1110.2.bb.c \(4\) \(8.863\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1+\cdots)q^{4}+\cdots\)
1110.2.bb.d \(28\) \(8.863\) None \(0\) \(0\) \(2\) \(0\)
1110.2.bb.e \(40\) \(8.863\) None \(0\) \(0\) \(2\) \(0\)

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

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