Properties

Label 100.3.f
Level $100$
Weight $3$
Character orbit 100.f
Rep. character $\chi_{100}(57,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $6$
Newform subspaces $2$
Sturm bound $45$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 100.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(45\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(100, [\chi])\).

Total New Old
Modular forms 78 6 72
Cusp forms 42 6 36
Eisenstein series 36 0 36

Trace form

\( 6q - 2q^{3} + 14q^{7} + O(q^{10}) \) \( 6q - 2q^{3} + 14q^{7} - 40q^{11} - 18q^{13} - 2q^{17} + 116q^{21} + 46q^{23} - 32q^{27} - 84q^{31} - 20q^{33} - 66q^{37} - 184q^{41} + 30q^{43} + 78q^{47} + 112q^{51} + 14q^{53} + 16q^{57} + 452q^{61} - 98q^{63} + 14q^{67} - 212q^{71} - 98q^{73} + 140q^{77} - 386q^{81} + 126q^{83} + 16q^{87} - 156q^{91} + 28q^{93} - 66q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
100.3.f.a \(2\) \(2.725\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(14\) \(q+(-1+i)q^{3}+(7+7i)q^{7}+7iq^{9}+\cdots\)
100.3.f.b \(4\) \(2.725\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+3\beta _{1}q^{3}-4\beta _{3}q^{7}+18\beta _{2}q^{9}-15q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(100, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)