Properties

Label 252.2.j
Level $252$
Weight $2$
Character orbit 252.j
Rep. character $\chi_{252}(85,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $2$
Sturm bound $96$
Trace bound $3$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(252, [\chi])\).

Total New Old
Modular forms 108 12 96
Cusp forms 84 12 72
Eisenstein series 24 0 24

Trace form

\( 12q + 2q^{5} + 4q^{9} + O(q^{10}) \) \( 12q + 2q^{5} + 4q^{9} + 4q^{11} - 2q^{15} + 4q^{17} + 12q^{19} - 2q^{21} - 8q^{23} + 14q^{29} + 6q^{31} + 8q^{33} - 8q^{35} - 12q^{37} - 20q^{39} + 6q^{41} - 6q^{43} - 10q^{45} - 6q^{47} - 6q^{49} - 22q^{51} - 24q^{53} - 12q^{55} - 30q^{57} - 28q^{59} - 18q^{65} + 32q^{69} + 4q^{71} + 12q^{73} + 46q^{75} + 8q^{77} + 6q^{79} - 32q^{81} - 2q^{83} + 30q^{85} - 68q^{87} + 36q^{89} - 12q^{91} + 22q^{93} + 4q^{95} + 24q^{97} - 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
252.2.j.a \(6\) \(2.012\) 6.0.309123.1 None \(0\) \(-2\) \(-1\) \(3\) \(q+(\beta _{2}+\beta _{4})q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots\)
252.2.j.b \(6\) \(2.012\) 6.0.309123.1 None \(0\) \(2\) \(3\) \(-3\) \(q+(1+\beta _{3}+\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)