Properties

Label 1224.2.bq
Level $1224$
Weight $2$
Character orbit 1224.bq
Rep. character $\chi_{1224}(145,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $92$
Newform subspaces $7$
Sturm bound $432$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1224.bq (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 7 \)
Sturm bound: \(432\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1224, [\chi])\).

Total New Old
Modular forms 928 92 836
Cusp forms 800 92 708
Eisenstein series 128 0 128

Trace form

\( 92 q + O(q^{10}) \) \( 92 q - 4 q^{11} + 8 q^{17} - 8 q^{25} - 16 q^{29} + 16 q^{31} + 32 q^{35} - 16 q^{41} - 28 q^{43} + 8 q^{49} + 24 q^{53} - 4 q^{59} + 24 q^{61} + 8 q^{65} + 72 q^{67} + 24 q^{71} + 8 q^{73} + 40 q^{79} + 28 q^{83} + 48 q^{85} + 16 q^{91} + 72 q^{95} - 20 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1224, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1224.2.bq.a 1224.bq 17.d $4$ $9.774$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-1+\zeta_{8})q^{5}+(-1-2\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1224.2.bq.b 1224.bq 17.d $4$ $9.774$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(8\) \(4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(2-2\zeta_{8}-\zeta_{8}^{2}-\zeta_{8}^{3})q^{5}+(1+\zeta_{8}+\cdots)q^{7}+\cdots\)
1224.2.bq.c 1224.bq 17.d $12$ $9.774$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q-\beta _{9}q^{5}+(1-\beta _{5}-\beta _{7}-\beta _{8}-\beta _{9}+\cdots)q^{7}+\cdots\)
1224.2.bq.d 1224.bq 17.d $16$ $9.774$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-1+\beta _{1}+\beta _{3}-\beta _{7}-\beta _{8}+\beta _{9}+\cdots)q^{5}+\cdots\)
1224.2.bq.e 1224.bq 17.d $16$ $9.774$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+(\beta _{4}+\beta _{7}-\beta _{14})q^{5}+(\beta _{1}+\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots\)
1224.2.bq.f 1224.bq 17.d $20$ $9.774$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q-\beta _{15}q^{5}-\beta _{18}q^{7}+(1-\beta _{1}+\beta _{4}+\cdots)q^{11}+\cdots\)
1224.2.bq.g 1224.bq 17.d $20$ $9.774$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta _{16}q^{5}-\beta _{17}q^{7}+\beta _{14}q^{11}-\beta _{5}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1224, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1224, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(612, [\chi])\)\(^{\oplus 2}\)