↑

Properties

Label 100.2.e
Level $100$
Weight $2$
Character orbit 100.e
Rep. character $\chi_{100}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $14$
Newform subspaces $4$
Sturm bound $30$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 100.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(30\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 42 22 20
Cusp forms 18 14 4
Eisenstein series 24 8 16

Trace form

\( 14 q + 2 q^{2} - 12 q^{6} - 4 q^{8} + O(q^{10}) \) \( 14 q + 2 q^{2} - 12 q^{6} - 4 q^{8} + 2 q^{13} + 4 q^{16} - 6 q^{17} + 6 q^{18} - 24 q^{21} - 20 q^{26} - 8 q^{32} + 12 q^{36} + 14 q^{37} + 8 q^{41} + 48 q^{46} + 4 q^{52} - 18 q^{53} + 48 q^{56} - 8 q^{58} - 72 q^{61} + 60 q^{66} + 12 q^{68} + 12 q^{72} + 22 q^{73} - 60 q^{76} + 90 q^{81} - 16 q^{82} - 72 q^{86} - 132 q^{96} - 26 q^{97} - 14 q^{98} + O(q^{100}) \)

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.e.a 100.e 20.e $2$ $0.799$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) \(-2\) \(-2\) \(0\) \(6\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+i)q^{2}+(-1-i)q^{3}-2iq^{4}+\cdots\)
100.2.e.b 100.e 20.e $2$ $0.799$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(2\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+i)q^{2}+2iq^{4}+(-2+2i)q^{8}+\cdots\)
100.2.e.c 100.e 20.e $2$ $0.799$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) \(2\) \(2\) \(0\) \(-6\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-i)q^{2}+(1+i)q^{3}-2iq^{4}+2q^{6}+\cdots\)
100.2.e.d 100.e 20.e $8$ $0.799$ 8.0.3317760000.5 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(-\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)