Properties

Label 100.9.k
Level $100$
Weight $9$
Character orbit 100.k
Rep. character $\chi_{100}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $160$
Newform subspaces $1$
Sturm bound $135$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
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: \(135\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(100, [\chi])\).

Total New Old
Modular forms 984 160 824
Cusp forms 936 160 776
Eisenstein series 48 0 48

Trace form

\( 160 q + 70 q^{3} - 894 q^{5} + 2030 q^{7} + O(q^{10}) \) \( 160 q + 70 q^{3} - 894 q^{5} + 2030 q^{7} - 33180 q^{13} + 48478 q^{15} - 414270 q^{17} + 718900 q^{19} - 207030 q^{23} + 1528574 q^{25} + 720310 q^{27} - 1956900 q^{29} + 6217120 q^{33} - 3418728 q^{35} - 14424480 q^{37} + 22510400 q^{39} + 4374720 q^{41} - 4033290 q^{43} + 13482846 q^{45} + 7278150 q^{47} - 15887760 q^{53} - 11288940 q^{55} + 39717680 q^{57} + 119809950 q^{59} + 18369120 q^{61} - 19887500 q^{63} + 136188762 q^{65} - 58954530 q^{67} - 128418850 q^{69} + 60703860 q^{71} + 33399920 q^{73} + 54011742 q^{75} + 184811940 q^{77} + 138506200 q^{79} + 196903220 q^{81} - 176936400 q^{83} - 186109196 q^{85} - 418946050 q^{87} + 442507050 q^{89} - 205667130 q^{93} + 256003896 q^{95} + 310913960 q^{97} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.9.k.a 100.k 25.f $160$ $40.738$ None 100.9.k.a \(0\) \(70\) \(-894\) \(2030\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{9}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(100, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)