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Properties

Label 100.7.k
Level $100$
Weight $7$
Character orbit 100.k
Rep. character $\chi_{100}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $120$
Newform subspaces $1$
Sturm bound $105$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 7 \)
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: \(105\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(100, [\chi])\).

Total New Old
Modular forms 744 120 624
Cusp forms 696 120 576
Eisenstein series 48 0 48

Trace form

\( 120 q - 32 q^{3} + 156 q^{5} + 264 q^{7} + O(q^{10}) \) \( 120 q - 32 q^{3} + 156 q^{5} + 264 q^{7} - 858 q^{13} + 7768 q^{15} - 1202 q^{17} - 19200 q^{19} + 9936 q^{23} - 29106 q^{25} - 1112 q^{27} - 24800 q^{29} - 21800 q^{33} - 35288 q^{35} + 29694 q^{37} + 414800 q^{39} - 108560 q^{41} - 216960 q^{43} - 816474 q^{45} - 116032 q^{47} + 605854 q^{53} + 898440 q^{55} - 366544 q^{57} - 67600 q^{59} + 388440 q^{61} - 1650128 q^{63} + 116362 q^{65} + 996384 q^{67} + 2802800 q^{69} - 758880 q^{71} + 960282 q^{73} - 3181128 q^{75} - 5241800 q^{77} - 2289600 q^{79} + 2640590 q^{81} + 1591736 q^{83} + 4579644 q^{85} + 5490416 q^{87} + 4375850 q^{89} - 7741752 q^{93} - 6884344 q^{95} - 4406046 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.7.k.a 100.k 25.f $120$ $23.005$ None 100.7.k.a \(0\) \(-32\) \(156\) \(264\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{7}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(100, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)