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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(100))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
100.2.a.a \(1\) \(0.799\) \(\Q\) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(+\) \(q+2q^{3}-2q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots\)

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 2 T + 3 T^{2} \)
$5$ 1
$7$ \( 1 + 2 T + 7 T^{2} \)
$11$ \( 1 + 11 T^{2} \)
$13$ \( 1 + 2 T + 13 T^{2} \)
$17$ \( 1 - 6 T + 17 T^{2} \)
$19$ \( 1 + 4 T + 19 T^{2} \)
$23$ \( 1 + 6 T + 23 T^{2} \)
$29$ \( 1 - 6 T + 29 T^{2} \)
$31$ \( 1 + 4 T + 31 T^{2} \)
$37$ \( 1 + 2 T + 37 T^{2} \)
$41$ \( 1 - 6 T + 41 T^{2} \)
$43$ \( 1 - 10 T + 43 T^{2} \)
$47$ \( 1 - 6 T + 47 T^{2} \)
$53$ \( 1 - 6 T + 53 T^{2} \)
$59$ \( 1 - 12 T + 59 T^{2} \)
$61$ \( 1 - 2 T + 61 T^{2} \)
$67$ \( 1 + 2 T + 67 T^{2} \)
$71$ \( 1 + 12 T + 71 T^{2} \)
$73$ \( 1 + 2 T + 73 T^{2} \)
$79$ \( 1 - 8 T + 79 T^{2} \)
$83$ \( 1 + 6 T + 83 T^{2} \)
$89$ \( 1 + 6 T + 89 T^{2} \)
$97$ \( 1 + 2 T + 97 T^{2} \)
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