Properties

Label 441.3.q
Level $441$
Weight $3$
Character orbit 441.q
Rep. character $\chi_{441}(116,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $52$
Newform subspaces $5$
Sturm bound $168$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 441.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(168\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(2\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(441, [\chi])\).

Total New Old
Modular forms 256 52 204
Cusp forms 192 52 140
Eisenstein series 64 0 64

Trace form

\( 52 q + 48 q^{4} + O(q^{10}) \) \( 52 q + 48 q^{4} + 16 q^{10} + 52 q^{13} - 88 q^{16} - 26 q^{19} - 104 q^{22} + 22 q^{25} - 22 q^{31} + 528 q^{34} + 238 q^{37} - 300 q^{40} + 140 q^{43} - 236 q^{46} - 252 q^{52} - 16 q^{55} - 104 q^{58} + 136 q^{61} - 1096 q^{64} - 422 q^{67} + 482 q^{73} + 504 q^{76} + 386 q^{79} + 212 q^{82} + 448 q^{85} + 336 q^{88} - 612 q^{94} - 568 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
441.3.q.a \(8\) \(12.016\) 8.0.\(\cdots\).5 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{3}+\beta _{6})q^{4}-2\beta _{1}q^{5}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
441.3.q.b \(8\) \(12.016\) 8.0.\(\cdots\).5 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{3}+\beta _{6})q^{4}+2\beta _{1}q^{5}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
441.3.q.c \(8\) \(12.016\) 8.0.\(\cdots\).5 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(4-4\beta _{3}+\beta _{5}+\beta _{7})q^{4}+\cdots\)
441.3.q.d \(12\) \(12.016\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-3\beta _{6}+\beta _{9})q^{4}+\beta _{4}q^{5}+\cdots\)
441.3.q.e \(16\) \(12.016\) 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{8}q^{2}+(2\beta _{1}+\beta _{10})q^{4}+\beta _{4}q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)