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Properties

Label 110.4.a
Level $110$
Weight $4$
Character orbit 110.a
Rep. character $\chi_{110}(1,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $9$
Sturm bound $72$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 110 = 2 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 110.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(72\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(110))\).

Total New Old
Modular forms 58 10 48
Cusp forms 50 10 40
Eisenstein series 8 0 8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)\(11\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(2\)
Plus space\(+\)\(8\)
Minus space\(-\)\(2\)

Trace form

\( 10 q + 12 q^{3} + 40 q^{4} - 10 q^{5} - 8 q^{6} + 8 q^{7} + 118 q^{9} + 48 q^{12} + 200 q^{13} + 88 q^{14} + 160 q^{16} - 128 q^{17} + 312 q^{19} - 40 q^{20} + 272 q^{21} - 44 q^{22} - 60 q^{23} - 32 q^{24}+ \cdots - 2048 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(110))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 11
110.4.a.a 110.a 1.a $1$ $6.490$ \(\Q\) None 110.4.a.a \(-2\) \(-7\) \(5\) \(-35\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-7q^{3}+4q^{4}+5q^{5}+14q^{6}+\cdots\)
110.4.a.b 110.a 1.a $1$ $6.490$ \(\Q\) None 110.4.a.b \(-2\) \(4\) \(-5\) \(-30\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
110.4.a.c 110.a 1.a $1$ $6.490$ \(\Q\) None 110.4.a.c \(-2\) \(4\) \(5\) \(20\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{3}+4q^{4}+5q^{5}-8q^{6}+\cdots\)
110.4.a.d 110.a 1.a $1$ $6.490$ \(\Q\) None 110.4.a.d \(2\) \(-8\) \(-5\) \(26\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-8q^{3}+4q^{4}-5q^{5}-2^{4}q^{6}+\cdots\)
110.4.a.e 110.a 1.a $1$ $6.490$ \(\Q\) None 110.4.a.e \(2\) \(-4\) \(-5\) \(-22\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
110.4.a.f 110.a 1.a $1$ $6.490$ \(\Q\) None 110.4.a.f \(2\) \(1\) \(5\) \(23\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+4q^{4}+5q^{5}+2q^{6}+\cdots\)
110.4.a.g 110.a 1.a $1$ $6.490$ \(\Q\) None 110.4.a.g \(2\) \(7\) \(-5\) \(11\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+7q^{3}+4q^{4}-5q^{5}+14q^{6}+\cdots\)
110.4.a.h 110.a 1.a $1$ $6.490$ \(\Q\) None 110.4.a.h \(2\) \(8\) \(5\) \(-12\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+8q^{3}+4q^{4}+5q^{5}+2^{4}q^{6}+\cdots\)
110.4.a.i 110.a 1.a $2$ $6.490$ \(\Q(\sqrt{177}) \) None 110.4.a.i \(-4\) \(7\) \(-10\) \(27\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(4-\beta )q^{3}+4q^{4}-5q^{5}+(-8+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(110))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(110)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)