Properties

Label 3528.2.bl
Level $3528$
Weight $2$
Character orbit 3528.bl
Rep. character $\chi_{3528}(521,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $4$
Sturm bound $1344$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3528.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(1344\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3528, [\chi])\).

Total New Old
Modular forms 1472 80 1392
Cusp forms 1216 80 1136
Eisenstein series 256 0 256

Trace form

\( 80 q + O(q^{10}) \) \( 80 q - 12 q^{19} - 68 q^{25} - 24 q^{31} + 4 q^{37} - 24 q^{43} + 36 q^{67} + 60 q^{73} + 32 q^{79} + 96 q^{85} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3528, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3528.2.bl.a 3528.bl 21.g $16$ $28.171$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{4}-\beta _{10})q^{5}+(\beta _{2}-\beta _{11}+\beta _{12}+\cdots)q^{11}+\cdots\)
3528.2.bl.b 3528.bl 21.g $16$ $28.171$ \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{48}^{4}q^{5}+(\zeta_{48}-\zeta_{48}^{3}-\zeta_{48}^{5}+\cdots)q^{11}+\cdots\)
3528.2.bl.c 3528.bl 21.g $16$ $28.171$ \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{48}^{4}-\zeta_{48}^{15})q^{5}+(\zeta_{48}-\zeta_{48}^{5}+\cdots)q^{11}+\cdots\)
3528.2.bl.d 3528.bl 21.g $32$ $28.171$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 2}\)