↑

Properties

Label 100.2.g
Level $100$
Weight $2$
Character orbit 100.g
Rep. character $\chi_{100}(21,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $12$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
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: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(100, [\chi])\).

Total New Old
Modular forms 72 12 60
Cusp forms 48 12 36
Eisenstein series 24 0 24

Trace form

\( 12 q + 2 q^{3} - 4 q^{5} - 2 q^{7} - 3 q^{9} + O(q^{10}) \) \( 12 q + 2 q^{3} - 4 q^{5} - 2 q^{7} - 3 q^{9} - 5 q^{11} - 2 q^{13} + 18 q^{15} + q^{17} - 8 q^{19} + 2 q^{21} - 6 q^{23} - 26 q^{25} - 34 q^{27} - 18 q^{29} + 12 q^{31} - 35 q^{33} - 3 q^{35} + 13 q^{37} + 22 q^{39} - 23 q^{41} + 50 q^{43} + 71 q^{45} + q^{47} + 34 q^{49} + 14 q^{51} + 21 q^{53} + 5 q^{55} + 72 q^{57} + 9 q^{59} - 26 q^{61} - 32 q^{63} - 18 q^{65} - 37 q^{67} - 44 q^{69} + 21 q^{71} + 18 q^{73} - 73 q^{75} - 60 q^{77} - 24 q^{79} + 18 q^{81} - 46 q^{83} - 16 q^{85} + 57 q^{87} - 2 q^{89} - 32 q^{91} + 22 q^{93} + 6 q^{95} - 7 q^{97} + 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.2.g.a 100.g 25.d $12$ $0.799$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(2\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{4}q^{3}+(-1-\beta _{4}+\beta _{5}-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

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