Properties

Label 196.2.e
Level $196$
Weight $2$
Character orbit 196.e
Rep. character $\chi_{196}(165,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $6$
Newform subspaces $2$
Sturm bound $56$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 196.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(56\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(196, [\chi])\).

Total New Old
Modular forms 80 6 74
Cusp forms 32 6 26
Eisenstein series 48 0 48

Trace form

\( 6q + q^{3} + 3q^{5} - 8q^{9} + O(q^{10}) \) \( 6q + q^{3} + 3q^{5} - 8q^{9} - 5q^{11} - 4q^{13} - 10q^{15} + 3q^{17} - q^{19} + 5q^{23} + 2q^{25} + 10q^{27} + 20q^{29} - 7q^{31} - 3q^{33} + 17q^{37} + 22q^{39} - 12q^{41} - 24q^{43} - 6q^{45} - 9q^{47} + 5q^{51} - 23q^{53} + 18q^{55} - 34q^{57} + 9q^{59} - q^{61} - 18q^{65} + 7q^{67} - 6q^{69} - q^{73} + 4q^{75} - 3q^{79} - 3q^{81} - 24q^{83} + 26q^{85} - 6q^{87} + 15q^{89} + 7q^{93} - 5q^{95} + 20q^{97} + 92q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(196, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
196.2.e.a \(2\) \(1.565\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(0\) \(q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(3+\cdots)q^{11}+\cdots\)
196.2.e.b \(4\) \(1.565\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(196, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(196, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)