Properties

Label 252.9.c
Level $252$
Weight $9$
Character orbit 252.c
Rep. character $\chi_{252}(197,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
Sturm bound $432$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 252.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(432\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(252, [\chi])\).

Total New Old
Modular forms 396 16 380
Cusp forms 372 16 356
Eisenstein series 24 0 24

Trace form

\( 16q + O(q^{10}) \) \( 16q - 95480q^{13} - 287560q^{19} - 1754520q^{25} - 3554264q^{31} - 182920q^{37} + 8472416q^{43} + 13176688q^{49} - 18692072q^{55} + 34224568q^{61} + 22683096q^{67} + 2137296q^{73} - 90245624q^{79} - 56204456q^{85} - 25661888q^{91} + 134041152q^{97} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
252.9.c.a \(16\) \(102.659\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}-\beta _{2}q^{7}+(3\beta _{1}+5\beta _{9}+\beta _{10}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)