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Properties

Label 1110.2.x
Level $1110$
Weight $2$
Character orbit 1110.x
Rep. character $\chi_{1110}(751,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
Newform subspaces $5$
Sturm bound $456$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.x (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(456\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 472 56 416
Cusp forms 440 56 384
Eisenstein series 32 0 32

Trace form

\( 56q - 4q^{3} + 28q^{4} - 4q^{7} - 28q^{9} + O(q^{10}) \) \( 56q - 4q^{3} + 28q^{4} - 4q^{7} - 28q^{9} - 8q^{10} - 8q^{11} + 4q^{12} - 12q^{13} - 28q^{16} - 12q^{19} - 4q^{21} + 28q^{25} - 8q^{26} + 8q^{27} + 4q^{28} - 4q^{30} + 16q^{33} + 12q^{34} + 24q^{35} - 56q^{36} + 16q^{37} + 16q^{38} + 24q^{39} - 4q^{40} + 24q^{42} - 4q^{44} - 4q^{46} + 32q^{47} + 8q^{48} - 56q^{49} - 12q^{52} - 8q^{53} - 12q^{55} - 24q^{58} + 36q^{59} + 8q^{63} - 56q^{64} + 4q^{65} - 12q^{67} + 8q^{70} + 8q^{71} - 8q^{73} - 12q^{74} - 8q^{75} - 12q^{76} - 8q^{77} - 8q^{78} + 12q^{79} - 28q^{81} + 48q^{83} - 8q^{84} + 32q^{85} - 8q^{86} + 24q^{87} + 36q^{89} + 4q^{90} - 12q^{91} - 24q^{92} - 84q^{93} + 24q^{94} - 16q^{95} - 48q^{98} + 4q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.x.a \(4\) \(8.863\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(2\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+\cdots)q^{5}+\cdots\)
1110.2.x.b \(4\) \(8.863\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(2\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+(\zeta_{12}+\cdots)q^{5}+\cdots\)
1110.2.x.c \(16\) \(8.863\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-8\) \(0\) \(-2\) \(q+(-\beta _{6}+\beta _{10})q^{2}+\beta _{9}q^{3}-\beta _{9}q^{4}+\cdots\)
1110.2.x.d \(16\) \(8.863\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-8\) \(0\) \(-2\) \(q+(\beta _{3}+\beta _{5})q^{2}-\beta _{9}q^{3}+\beta _{9}q^{4}+\beta _{3}q^{5}+\cdots\)
1110.2.x.e \(16\) \(8.863\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(8\) \(0\) \(-4\) \(q+\beta _{6}q^{2}-\beta _{1}q^{3}-\beta _{1}q^{4}-\beta _{7}q^{5}+\cdots\)

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

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