Properties

Label 252.3.z
Level $252$
Weight $3$
Character orbit 252.z
Rep. character $\chi_{252}(73,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $14$
Newform subspaces $5$
Sturm bound $144$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 252.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(144\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(252, [\chi])\).

Total New Old
Modular forms 216 14 202
Cusp forms 168 14 154
Eisenstein series 48 0 48

Trace form

\( 14 q + 3 q^{5} + 4 q^{7} + O(q^{10}) \) \( 14 q + 3 q^{5} + 4 q^{7} - 3 q^{11} - 3 q^{17} + 45 q^{19} - 21 q^{23} + 68 q^{25} + 108 q^{29} + 105 q^{31} + 99 q^{35} + 35 q^{37} - 136 q^{43} - 141 q^{47} - 100 q^{49} - 105 q^{53} - 231 q^{59} + 39 q^{61} - 90 q^{65} - 77 q^{67} + 456 q^{71} - 99 q^{73} + 147 q^{77} + 115 q^{79} - 522 q^{85} - 423 q^{89} - 318 q^{91} - 69 q^{95} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
252.3.z.a 252.z 7.d $2$ $6.867$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-14\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\zeta_{6})q^{5}-7q^{7}+(15-15\zeta_{6})q^{11}+\cdots\)
252.3.z.b 252.z 7.d $2$ $6.867$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(13\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\zeta_{6})q^{5}+(5+3\zeta_{6})q^{7}+(-3+\cdots)q^{11}+\cdots\)
252.3.z.c 252.z 7.d $2$ $6.867$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-11\) $\mathrm{U}(1)[D_{6}]$ \(q+(-8+5\zeta_{6})q^{7}+(-15+30\zeta_{6})q^{13}+\cdots\)
252.3.z.d 252.z 7.d $4$ $6.867$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(0\) \(0\) \(0\) \(14\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{5}+(7+7\beta _{1})q^{7}+(-2\beta _{2}+\beta _{3})q^{11}+\cdots\)
252.3.z.e 252.z 7.d $4$ $6.867$ \(\Q(\sqrt{-3}, \sqrt{65})\) None \(0\) \(0\) \(9\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2+\beta _{1}-\beta _{3})q^{5}+(1-\beta _{2})q^{7}+(-8\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

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