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Properties

Label 100.2.a
Level $100$
Weight $2$
Character orbit 100.a
Rep. character $\chi_{100}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 100.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(100))\).

Total New Old
Modular forms 24 1 23
Cusp forms 7 1 6
Eisenstein series 17 0 17

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

\(2\)\(5\)FrickeDim
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q + 2 q^{3} - 2 q^{7} + q^{9} + O(q^{10}) \) \( q + 2 q^{3} - 2 q^{7} + q^{9} - 2 q^{13} + 6 q^{17} - 4 q^{19} - 4 q^{21} - 6 q^{23} - 4 q^{27} + 6 q^{29} - 4 q^{31} - 2 q^{37} - 4 q^{39} + 6 q^{41} + 10 q^{43} + 6 q^{47} - 3 q^{49} + 12 q^{51} + 6 q^{53} - 8 q^{57} + 12 q^{59} + 2 q^{61} - 2 q^{63} - 2 q^{67} - 12 q^{69} - 12 q^{71} - 2 q^{73} + 8 q^{79} - 11 q^{81} - 6 q^{83} + 12 q^{87} - 6 q^{89} + 4 q^{91} - 8 q^{93} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(100))\) 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
100.2.a.a 100.a 1.a $1$ $0.799$ \(\Q\) None 20.2.a.a \(0\) \(2\) \(0\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(100)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)