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

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

Decomposition of \(S_{2}^{\mathrm{new}}(1110, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1110.2.d.a 1110.d 5.b $2$ $8.863$ \(\Q(\sqrt{-1}) \) None 1110.2.d.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+(-2-i)q^{5}+\cdots\)
1110.2.d.b 1110.d 5.b $2$ $8.863$ \(\Q(\sqrt{-1}) \) None 1110.2.d.b \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+(-1+2i)q^{5}+\cdots\)
1110.2.d.c 1110.d 5.b $2$ $8.863$ \(\Q(\sqrt{-1}) \) None 1110.2.d.c \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+(1-2i)q^{5}+q^{6}+\cdots\)
1110.2.d.d 1110.d 5.b $2$ $8.863$ \(\Q(\sqrt{-1}) \) None 1110.2.d.d \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}-q^{6}+\cdots\)
1110.2.d.e 1110.d 5.b $2$ $8.863$ \(\Q(\sqrt{-1}) \) None 1110.2.d.e \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}+q^{6}+\cdots\)
1110.2.d.f 1110.d 5.b $4$ $8.863$ \(\Q(i, \sqrt{5})\) None 1110.2.d.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}+\beta _{2}q^{5}-q^{6}+\cdots\)
1110.2.d.g 1110.d 5.b $4$ $8.863$ \(\Q(\zeta_{8})\) None 1110.2.d.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{2}q^{3}-q^{4}+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
1110.2.d.h 1110.d 5.b $4$ $8.863$ \(\Q(i, \sqrt{6})\) None 1110.2.d.h \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
1110.2.d.i 1110.d 5.b $6$ $8.863$ 6.0.5161984.1 None 1110.2.d.i \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-\beta _{4}q^{3}-q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
1110.2.d.j 1110.d 5.b $8$ $8.863$ 8.0.\(\cdots\).2 None 1110.2.d.j \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}+(\beta _{1}+\beta _{5})q^{5}+\cdots\)

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

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