Properties

Label 252.4.k
Level $252$
Weight $4$
Character orbit 252.k
Rep. character $\chi_{252}(37,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $6$
Sturm bound $192$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(192\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(252, [\chi])\).

Total New Old
Modular forms 312 20 292
Cusp forms 264 20 244
Eisenstein series 48 0 48

Trace form

\( 20q - 6q^{5} + 4q^{7} + O(q^{10}) \) \( 20q - 6q^{5} + 4q^{7} - 24q^{11} - 30q^{17} + 40q^{19} - 48q^{23} - 332q^{25} - 168q^{31} + 360q^{35} + 346q^{37} + 816q^{41} - 176q^{43} + 48q^{47} - 844q^{49} + 342q^{53} - 656q^{55} - 1152q^{59} + 918q^{61} - 1260q^{65} + 152q^{67} - 2184q^{71} + 1262q^{73} + 2154q^{77} + 192q^{79} + 2832q^{83} + 2572q^{85} - 858q^{89} - 1992q^{91} + 1272q^{95} - 976q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
252.4.k.a \(2\) \(14.868\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-37\) \(q+(-19+\zeta_{6})q^{7}+89q^{13}+(163-163\zeta_{6})q^{19}+\cdots\)
252.4.k.b \(2\) \(14.868\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(17\) \(q+(-1+19\zeta_{6})q^{7}-19q^{13}+(-107+\cdots)q^{19}+\cdots\)
252.4.k.c \(4\) \(14.868\) \(\Q(\sqrt{-3}, \sqrt{37})\) None \(0\) \(0\) \(-14\) \(24\) \(q+(-7\beta _{1}-2\beta _{2})q^{5}+(10-8\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
252.4.k.d \(4\) \(14.868\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(0\) \(-3\) \(-20\) \(q+(-2+2\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
252.4.k.e \(4\) \(14.868\) \(\Q(\sqrt{-3}, \sqrt{385})\) None \(0\) \(0\) \(0\) \(14\) \(q-\beta _{2}q^{5}+(-7+21\beta _{1})q^{7}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
252.4.k.f \(4\) \(14.868\) \(\Q(\sqrt{-3}, \sqrt{193})\) None \(0\) \(0\) \(11\) \(6\) \(q+(-\beta _{1}+6\beta _{2})q^{5}+(-1+2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)