Properties

Label 1110.2.i
Level $1110$
Weight $2$
Character orbit 1110.i
Rep. character $\chi_{1110}(121,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $56$
Newform subspaces $16$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 16 \)
Sturm bound: \(456\)
Trace bound: \(7\)
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 56 416
Cusp forms 440 56 384
Eisenstein series 32 0 32

Trace form

\( 56q - 4q^{3} - 28q^{4} + 4q^{7} - 28q^{9} + O(q^{10}) \) \( 56q - 4q^{3} - 28q^{4} + 4q^{7} - 28q^{9} + 8q^{10} - 8q^{11} - 4q^{12} + 4q^{13} + 16q^{14} - 28q^{16} - 16q^{17} + 4q^{19} + 4q^{21} - 16q^{23} - 28q^{25} - 8q^{26} + 8q^{27} + 4q^{28} + 16q^{29} - 4q^{30} + 24q^{31} + 12q^{34} + 56q^{36} + 16q^{38} + 16q^{39} - 4q^{40} - 32q^{41} + 8q^{42} + 8q^{43} + 4q^{44} - 12q^{46} + 32q^{47} + 8q^{48} - 24q^{49} - 32q^{51} + 4q^{52} - 8q^{53} - 12q^{55} - 8q^{56} - 24q^{57} - 24q^{58} - 20q^{59} + 8q^{61} - 8q^{63} + 56q^{64} + 4q^{65} - 8q^{66} + 12q^{67} + 32q^{68} + 16q^{69} - 8q^{70} + 24q^{71} + 8q^{73} - 12q^{74} + 8q^{75} + 4q^{76} + 40q^{77} - 8q^{78} - 44q^{79} - 28q^{81} - 16q^{82} + 16q^{83} - 8q^{84} + 8q^{86} - 8q^{87} - 12q^{89} - 4q^{90} - 20q^{91} + 8q^{92} + 28q^{93} + 8q^{94} - 16q^{95} - 56q^{97} + 16q^{98} + 4q^{99} + O(q^{100}) \)

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.i.a \(2\) \(8.863\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(4\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
1110.2.i.b \(2\) \(8.863\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(-3\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
1110.2.i.c \(2\) \(8.863\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-2\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
1110.2.i.d \(2\) \(8.863\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(1\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
1110.2.i.e \(2\) \(8.863\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(3\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
1110.2.i.f \(2\) \(8.863\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(-2\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
1110.2.i.g \(2\) \(8.863\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(0\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
1110.2.i.h \(2\) \(8.863\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(5\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
1110.2.i.i \(4\) \(8.863\) \(\Q(\sqrt{-3}, \sqrt{145})\) None \(-2\) \(-2\) \(2\) \(-2\) \(q+(-1+\beta _{2})q^{2}-\beta _{2}q^{3}-\beta _{2}q^{4}+\beta _{2}q^{5}+\cdots\)
1110.2.i.j \(4\) \(8.863\) \(\Q(\sqrt{-3}, \sqrt{73})\) None \(-2\) \(2\) \(-2\) \(0\) \(q-\beta _{2}q^{2}+(1-\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
1110.2.i.k \(4\) \(8.863\) \(\Q(\sqrt{-3}, \sqrt{41})\) None \(2\) \(-2\) \(-2\) \(6\) \(q+(1-\beta _{2})q^{2}-\beta _{2}q^{3}-\beta _{2}q^{4}-\beta _{2}q^{5}+\cdots\)
1110.2.i.l \(4\) \(8.863\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(2\) \(-2\) \(2\) \(-2\) \(q+(1-\beta _{1})q^{2}-\beta _{1}q^{3}-\beta _{1}q^{4}+\beta _{1}q^{5}+\cdots\)
1110.2.i.m \(4\) \(8.863\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(-2\) \(2\) \(-1\) \(q+(1-\beta _{1})q^{2}-\beta _{1}q^{3}-\beta _{1}q^{4}+\beta _{1}q^{5}+\cdots\)
1110.2.i.n \(4\) \(8.863\) \(\Q(\zeta_{12})\) None \(2\) \(2\) \(-2\) \(-2\) \(q+(1-\zeta_{12})q^{2}+\zeta_{12}q^{3}-\zeta_{12}q^{4}+\cdots\)
1110.2.i.o \(6\) \(8.863\) 6.0.45911232.1 None \(-3\) \(3\) \(3\) \(-1\) \(q-\beta _{4}q^{2}+(1-\beta _{4})q^{3}+(-1+\beta _{4})q^{4}+\cdots\)
1110.2.i.p \(10\) \(8.863\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-5\) \(-5\) \(-5\) \(0\) \(q+(-1-\beta _{6})q^{2}+\beta _{6}q^{3}+\beta _{6}q^{4}+\beta _{6}q^{5}+\cdots\)

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

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