Properties

Label 1110.2.h
Level $1110$
Weight $2$
Character orbit 1110.h
Rep. character $\chi_{1110}(961,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $7$
Sturm bound $456$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(456\)
Trace bound: \(7\)
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 28 208
Cusp forms 220 28 192
Eisenstein series 16 0 16

Trace form

\( 28q + 4q^{3} - 28q^{4} - 8q^{7} + 28q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 28q^{4} - 8q^{7} + 28q^{9} - 4q^{10} + 8q^{11} - 4q^{12} + 28q^{16} - 8q^{21} - 28q^{25} + 8q^{26} + 4q^{27} + 8q^{28} + 4q^{30} + 8q^{33} + 24q^{34} - 28q^{36} + 20q^{37} + 8q^{38} + 4q^{40} - 8q^{44} - 8q^{46} + 16q^{47} + 4q^{48} - 4q^{49} + 8q^{53} + 24q^{58} - 24q^{62} - 8q^{63} - 28q^{64} + 8q^{65} - 8q^{70} + 16q^{71} + 32q^{73} - 12q^{74} - 4q^{75} - 16q^{77} + 8q^{78} + 28q^{81} + 48q^{83} + 8q^{84} - 8q^{85} + 8q^{86} - 4q^{90} + 16q^{95} + 8q^{99} + O(q^{100}) \)

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.h.a \(2\) \(8.863\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(-2\) \(q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}-q^{7}+\cdots\)
1110.2.h.b \(2\) \(8.863\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(4\) \(q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}+2q^{7}+\cdots\)
1110.2.h.c \(2\) \(8.863\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(2\) \(q+iq^{2}+q^{3}-q^{4}+iq^{5}+iq^{6}+q^{7}+\cdots\)
1110.2.h.d \(4\) \(8.863\) \(\Q(i, \sqrt{73})\) None \(0\) \(-4\) \(0\) \(-4\) \(q-\beta _{2}q^{2}-q^{3}-q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots\)
1110.2.h.e \(4\) \(8.863\) \(\Q(i, \sqrt{33})\) None \(0\) \(-4\) \(0\) \(2\) \(q+\beta _{2}q^{2}-q^{3}-q^{4}+\beta _{2}q^{5}-\beta _{2}q^{6}+\cdots\)
1110.2.h.f \(6\) \(8.863\) 6.0.279290944.1 None \(0\) \(6\) \(0\) \(-6\) \(q+\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots\)
1110.2.h.g \(8\) \(8.863\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(8\) \(0\) \(-4\) \(q-\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{5}-\beta _{2}q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)