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Properties

Label 1100.1.x
Level $1100$
Weight $1$
Character orbit 1100.x
Rep. character $\chi_{1100}(21,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $8$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1100.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1100, [\chi])\).

Total New Old
Modular forms 44 8 36
Cusp forms 20 8 12
Eisenstein series 24 0 24

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + 2 q^{3} - 4 q^{5} - 2 q^{11} - q^{15} + 2 q^{23} - 4 q^{25} - 7 q^{27} + 2 q^{31} + 2 q^{33} + 2 q^{37} - 4 q^{47} + 8 q^{49} - 4 q^{53} + q^{55} - 3 q^{59} - 3 q^{67} - 7 q^{69} + 2 q^{71} - q^{75}+ \cdots + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(1100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1100.1.x.a 1100.x 275.v $8$ $0.549$ \(\Q(\zeta_{15})\) $D_{15}$ \(\Q(\sqrt{-11}) \) None 1100.1.x.a \(0\) \(2\) \(-4\) \(0\) \(q+(\zeta_{30}^{2}+\zeta_{30}^{4})q^{3}-\zeta_{30}^{5}q^{5}+(\zeta_{30}^{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1100, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1100, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)