Properties

Label 252.9.d
Level $252$
Weight $9$
Character orbit 252.d
Rep. character $\chi_{252}(181,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $4$
Sturm bound $432$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 252.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(432\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 396 26 370
Cusp forms 372 26 346
Eisenstein series 24 0 24

Trace form

\( 26 q + 1870 q^{7} + O(q^{10}) \) \( 26 q + 1870 q^{7} + 13104 q^{11} + 33984 q^{23} - 2355862 q^{25} - 955440 q^{29} + 2795400 q^{35} - 798724 q^{37} + 4749788 q^{43} - 12584902 q^{49} + 8469792 q^{53} + 22705776 q^{65} + 12334564 q^{67} + 35103312 q^{71} + 12620304 q^{77} + 20380804 q^{79} - 4798896 q^{85} + 29955600 q^{91} - 189214992 q^{95} + O(q^{100}) \)

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.d.a \(2\) \(102.659\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4034\) \(q+(-2017-47\zeta_{6})q^{7}-1606\zeta_{6}q^{13}+\cdots\)
252.9.d.b \(6\) \(102.659\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(2166\) \(q-\beta _{1}q^{5}+(19^{2}-\beta _{3})q^{7}+(-4082+\cdots)q^{11}+\cdots\)
252.9.d.c \(8\) \(102.659\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(6076\) \(q-\beta _{1}q^{5}+(756-7\beta _{2})q^{7}-\beta _{5}q^{11}+\cdots\)
252.9.d.d \(10\) \(102.659\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(-2338\) \(q+(\beta _{1}+\beta _{6})q^{5}+(-234-2\beta _{1}+\beta _{7}+\cdots)q^{7}+\cdots\)

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

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