Properties

Label 100.6.g
Level $100$
Weight $6$
Character orbit 100.g
Rep. character $\chi_{100}(21,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $52$
Newform subspaces $1$
Sturm bound $90$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 100.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 1 \)
Sturm bound: \(90\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(100, [\chi])\).

Total New Old
Modular forms 312 52 260
Cusp forms 288 52 236
Eisenstein series 24 0 24

Trace form

\( 52 q + 2 q^{3} + 116 q^{5} - 42 q^{7} - 1153 q^{9} + O(q^{10}) \) \( 52 q + 2 q^{3} + 116 q^{5} - 42 q^{7} - 1153 q^{9} - 5 q^{11} + 1458 q^{13} + 2418 q^{15} - 2329 q^{17} + 1912 q^{19} - 4818 q^{21} + 3594 q^{23} + 934 q^{25} + 3206 q^{27} - 1458 q^{29} + 5532 q^{31} + 2435 q^{33} - 5603 q^{35} + 22043 q^{37} - 9938 q^{39} + 4567 q^{41} - 35390 q^{43} - 59359 q^{45} - 5859 q^{47} + 165974 q^{49} + 68014 q^{51} + 20151 q^{53} - 97855 q^{55} - 241368 q^{57} - 116271 q^{59} + 39134 q^{61} + 262808 q^{63} + 190502 q^{65} + 40883 q^{67} - 51844 q^{69} - 109999 q^{71} - 187802 q^{73} - 164833 q^{75} + 102220 q^{77} + 122216 q^{79} - 264922 q^{81} + 125394 q^{83} + 83764 q^{85} + 205117 q^{87} - 107222 q^{89} + 58608 q^{91} - 490158 q^{93} - 82634 q^{95} + 129683 q^{97} + 302280 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.6.g.a 100.g 25.d $52$ $16.038$ None \(0\) \(2\) \(116\) \(-42\) $\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{6}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(100, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)