Properties

Label 441.5.b
Level $441$
Weight $5$
Character orbit 441.b
Rep. character $\chi_{441}(197,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $7$
Sturm bound $280$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 441.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(280\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(2\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(441, [\chi])\).

Total New Old
Modular forms 240 54 186
Cusp forms 208 54 154
Eisenstein series 32 0 32

Trace form

\( 54 q - 388 q^{4} + O(q^{10}) \) \( 54 q - 388 q^{4} + 124 q^{10} + 584 q^{13} + 1744 q^{16} - 232 q^{19} - 416 q^{22} - 5982 q^{25} - 384 q^{31} + 6492 q^{34} + 56 q^{37} - 3504 q^{40} + 2100 q^{43} + 496 q^{46} - 36848 q^{52} - 3544 q^{55} + 7516 q^{58} - 11212 q^{61} + 16168 q^{64} - 3772 q^{67} - 35664 q^{73} + 8344 q^{76} - 21492 q^{79} + 9260 q^{82} + 55636 q^{85} + 52248 q^{88} - 80616 q^{94} + 19200 q^{97} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
441.5.b.a 441.b 3.b $2$ $45.586$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2q^{4}+7\beta q^{5}+14\beta q^{8}-126q^{10}+\cdots\)
441.5.b.b 441.b 3.b $4$ $45.586$ \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}+(-2^{4}+\beta _{3})q^{4}+(-31\beta _{1}+\cdots)q^{8}+\cdots\)
441.5.b.c 441.b 3.b $4$ $45.586$ \(\Q(\sqrt{-2}, \sqrt{93})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+14q^{4}+\beta _{3}q^{5}+30\beta _{1}q^{8}+\cdots\)
441.5.b.d 441.b 3.b $8$ $45.586$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-15+\beta _{2})q^{4}+(2\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots\)
441.5.b.e 441.b 3.b $10$ $45.586$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-6+\beta _{3})q^{4}-\beta _{6}q^{5}+(-6\beta _{1}+\cdots)q^{8}+\cdots\)
441.5.b.f 441.b 3.b $10$ $45.586$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-6+\beta _{3})q^{4}+\beta _{6}q^{5}+(-6\beta _{1}+\cdots)q^{8}+\cdots\)
441.5.b.g 441.b 3.b $16$ $45.586$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{2}+(-8-\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)