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Properties

Label 100.3.k
Level $100$
Weight $3$
Character orbit 100.k
Rep. character $\chi_{100}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $40$
Newform subspaces $1$
Sturm bound $45$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 100.k (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(45\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(100, [\chi])\).

Total New Old
Modular forms 264 40 224
Cusp forms 216 40 176
Eisenstein series 48 0 48

Trace form

\( 40 q - 2 q^{3} + 6 q^{5} + 14 q^{7} + O(q^{10}) \) \( 40 q - 2 q^{3} + 6 q^{5} + 14 q^{7} - 18 q^{13} - 2 q^{15} + 68 q^{17} + 100 q^{19} + 66 q^{23} - 16 q^{25} - 122 q^{27} - 100 q^{29} - 200 q^{33} - 208 q^{35} - 126 q^{37} - 400 q^{39} + 80 q^{41} - 210 q^{43} - 264 q^{45} - 2 q^{47} + 194 q^{53} + 300 q^{55} + 656 q^{57} + 550 q^{59} - 120 q^{61} + 1012 q^{63} + 512 q^{65} + 294 q^{67} + 350 q^{69} - 60 q^{71} - 58 q^{73} - 18 q^{75} - 100 q^{77} - 200 q^{79} + 230 q^{81} - 824 q^{83} - 776 q^{85} - 1114 q^{87} - 800 q^{89} - 402 q^{93} - 224 q^{95} - 106 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.3.k.a 100.k 25.f $40$ $2.725$ None \(0\) \(-2\) \(6\) \(14\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{3}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(100, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)