Properties

Label 1110.2.d
Level $1110$
Weight $2$
Character orbit 1110.d
Rep. character $\chi_{1110}(889,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $10$
Sturm bound $456$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(456\)
Trace bound: \(6\)
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 236 36 200
Cusp forms 220 36 184
Eisenstein series 16 0 16

Trace form

\( 36q - 36q^{4} + 8q^{5} - 4q^{6} - 36q^{9} + O(q^{10}) \) \( 36q - 36q^{4} + 8q^{5} - 4q^{6} - 36q^{9} + 4q^{10} - 16q^{11} - 4q^{15} + 36q^{16} + 24q^{19} - 8q^{20} + 4q^{24} - 20q^{25} + 32q^{29} - 8q^{31} - 16q^{35} + 36q^{36} - 4q^{40} + 16q^{44} - 8q^{45} - 12q^{49} - 8q^{51} + 4q^{54} - 16q^{55} - 16q^{59} + 4q^{60} - 24q^{61} - 36q^{64} + 24q^{65} - 16q^{66} + 32q^{69} + 24q^{70} - 16q^{71} - 24q^{76} + 56q^{79} + 8q^{80} + 36q^{81} - 24q^{85} - 48q^{86} - 4q^{90} - 64q^{91} + 64q^{94} - 32q^{95} - 4q^{96} + 16q^{99} + O(q^{100}) \)

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.d.a \(2\) \(8.863\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+(-2-i)q^{5}+\cdots\)
1110.2.d.b \(2\) \(8.863\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+(-1+2i)q^{5}+\cdots\)
1110.2.d.c \(2\) \(8.863\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+(1-2i)q^{5}+q^{6}+\cdots\)
1110.2.d.d \(2\) \(8.863\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}-q^{6}+\cdots\)
1110.2.d.e \(2\) \(8.863\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}+q^{6}+\cdots\)
1110.2.d.f \(4\) \(8.863\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}+\beta _{2}q^{5}-q^{6}+\cdots\)
1110.2.d.g \(4\) \(8.863\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{2}q^{3}-q^{4}+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
1110.2.d.h \(4\) \(8.863\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
1110.2.d.i \(6\) \(8.863\) 6.0.5161984.1 None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{4}q^{2}-\beta _{4}q^{3}-q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
1110.2.d.j \(8\) \(8.863\) 8.0.\(\cdots\).2 None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}+(\beta _{1}+\beta _{5})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)