Properties

Label 100.4.a
Level $100$
Weight $4$
Character orbit 100.a
Rep. character $\chi_{100}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $4$
Sturm bound $60$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 100.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(100))\).

Total New Old
Modular forms 54 5 49
Cusp forms 36 5 31
Eisenstein series 18 0 18

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.
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(3\)
Minus space\(-\)\(2\)

Trace form

\( 5 q - 4 q^{3} + 16 q^{7} + 35 q^{9} + O(q^{10}) \) \( 5 q - 4 q^{3} + 16 q^{7} + 35 q^{9} + 70 q^{11} - 86 q^{13} - 18 q^{17} + 30 q^{19} + 140 q^{21} - 48 q^{23} + 152 q^{27} + 90 q^{29} - 220 q^{31} + 240 q^{33} - 254 q^{37} - 480 q^{39} - 200 q^{41} + 100 q^{43} - 168 q^{47} + 45 q^{49} - 910 q^{51} + 498 q^{53} - 176 q^{57} - 340 q^{59} + 70 q^{61} - 176 q^{63} + 1036 q^{67} + 1220 q^{69} + 1200 q^{71} - 506 q^{73} - 960 q^{77} - 1620 q^{79} + 1685 q^{81} - 948 q^{83} + 744 q^{87} + 2740 q^{89} - 704 q^{93} + 766 q^{97} + 280 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(100))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5
100.4.a.a 100.a 1.a $1$ $5.900$ \(\Q\) None \(0\) \(-4\) \(0\) \(16\) $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{3}+2^{4}q^{7}-11q^{9}-60q^{11}+\cdots\)
100.4.a.b 100.a 1.a $1$ $5.900$ \(\Q\) None \(0\) \(-1\) \(0\) \(-26\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-26q^{7}-26q^{9}+45q^{11}-44q^{13}+\cdots\)
100.4.a.c 100.a 1.a $1$ $5.900$ \(\Q\) None \(0\) \(1\) \(0\) \(26\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+26q^{7}-26q^{9}+45q^{11}+44q^{13}+\cdots\)
100.4.a.d 100.a 1.a $2$ $5.900$ \(\Q(\sqrt{19}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{7}+7^{2}q^{9}+20q^{11}-6\beta q^{13}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(100))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(100)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)