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Properties

Label 1110.2.u
Level $1110$
Weight $2$
Character orbit 1110.u
Rep. character $\chi_{1110}(191,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $6$
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.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 111 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(456\)
Trace bound: \(7\)
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 96 376
Cusp forms 440 96 344
Eisenstein series 32 0 32

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 24 q^{13} - 96 q^{16} + 24 q^{19} - 48 q^{31} + 16 q^{34} + 24 q^{37} + 32 q^{39} - 24 q^{42} + 56 q^{43} - 16 q^{45} + 112 q^{49} + 8 q^{51} + 24 q^{52} + 24 q^{55} - 48 q^{57} - 40 q^{61} - 48 q^{66} - 16 q^{69} - 24 q^{76} + 32 q^{79} + 32 q^{81} - 32 q^{82} + 48 q^{87} - 88 q^{93} + 8 q^{94} - 40 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1110.2.u.a 1110.u 111.g $4$ $8.863$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
1110.2.u.b 1110.u 111.g $4$ $8.863$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
1110.2.u.c 1110.u 111.g $4$ $8.863$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{3}q^{2}+(\zeta_{8}-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
1110.2.u.d 1110.u 111.g $4$ $8.863$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{3}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
1110.2.u.e 1110.u 111.g $40$ $8.863$ None \(0\) \(0\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{4}]$
1110.2.u.f 1110.u 111.g $40$ $8.863$ None \(0\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(1110, [\chi]) \cong \)