Properties

Label 1110.2.e
Level $1110$
Weight $2$
Character orbit 1110.e
Rep. character $\chi_{1110}(739,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $4$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(456\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\), \(13\)

Dimensions

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

Total New Old
Modular forms 236 36 200
Cusp forms 220 36 184
Eisenstein series 16 0 16

Trace form

\( 36q + 36q^{4} - 36q^{9} + O(q^{10}) \) \( 36q + 36q^{4} - 36q^{9} - 4q^{10} - 8q^{11} + 36q^{16} + 24q^{21} + 4q^{25} + 16q^{26} - 8q^{30} + 48q^{34} - 36q^{36} - 4q^{40} + 16q^{41} - 8q^{44} + 16q^{46} - 44q^{49} + 36q^{64} - 8q^{65} + 8q^{70} - 16q^{74} - 16q^{75} + 36q^{81} + 24q^{84} + 56q^{85} + 4q^{90} - 48q^{95} + 8q^{99} + O(q^{100}) \)

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.e.a \(2\) \(8.863\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(4\) \(0\) \(q-q^{2}-iq^{3}+q^{4}+(2-i)q^{5}+iq^{6}+\cdots\)
1110.2.e.b \(2\) \(8.863\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-4\) \(0\) \(q+q^{2}-iq^{3}+q^{4}+(-2+i)q^{5}-iq^{6}+\cdots\)
1110.2.e.c \(16\) \(8.863\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(0\) \(-2\) \(0\) \(q-q^{2}+\beta _{7}q^{3}+q^{4}-\beta _{11}q^{5}-\beta _{7}q^{6}+\cdots\)
1110.2.e.d \(16\) \(8.863\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(0\) \(2\) \(0\) \(q+q^{2}+\beta _{7}q^{3}+q^{4}+\beta _{11}q^{5}+\beta _{7}q^{6}+\cdots\)

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

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