Properties

Label 252.4.j
Level $252$
Weight $4$
Character orbit 252.j
Rep. character $\chi_{252}(85,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $36$
Newform subspaces $2$
Sturm bound $192$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(192\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 300 36 264
Cusp forms 276 36 240
Eisenstein series 24 0 24

Trace form

\( 36q + 6q^{3} + 8q^{5} - 74q^{9} + O(q^{10}) \) \( 36q + 6q^{3} + 8q^{5} - 74q^{9} - 98q^{11} + 208q^{15} + 76q^{17} - 180q^{19} - 56q^{21} - 284q^{23} - 594q^{25} - 900q^{27} - 676q^{29} - 36q^{31} + 446q^{33} + 280q^{35} - 144q^{37} + 508q^{39} - 246q^{41} - 342q^{43} - 1588q^{45} - 1176q^{47} - 882q^{49} + 1850q^{51} + 1488q^{53} - 792q^{55} - 258q^{57} + 302q^{59} + 588q^{63} - 1872q^{65} - 162q^{67} + 128q^{69} + 1984q^{71} - 828q^{73} - 2234q^{75} - 616q^{77} - 468q^{79} - 890q^{81} + 2164q^{83} - 2016q^{85} + 3856q^{87} + 720q^{89} + 504q^{91} + 700q^{93} + 3364q^{95} + 342q^{97} + 5956q^{99} + O(q^{100}) \)

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.j.a \(18\) \(14.868\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(-5\) \(14\) \(63\) \(q+\beta _{4}q^{3}+(2-2\beta _{2}+\beta _{12})q^{5}+7\beta _{2}q^{7}+\cdots\)
252.4.j.b \(18\) \(14.868\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(11\) \(-6\) \(-63\) \(q+(1-\beta _{1})q^{3}+(-1+\beta _{2}+\beta _{3})q^{5}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)