Properties

Label 912.3.b
Level $912$
Weight $3$
Character orbit 912.b
Rep. character $\chi_{912}(911,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $8$
Sturm bound $480$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 912.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 228 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(480\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(7\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(912, [\chi])\).

Total New Old
Modular forms 332 80 252
Cusp forms 308 80 228
Eisenstein series 24 0 24

Trace form

\( 80 q + 24 q^{9} + O(q^{10}) \) \( 80 q + 24 q^{9} - 400 q^{25} - 544 q^{49} - 96 q^{57} - 112 q^{61} - 64 q^{73} + 312 q^{81} + 96 q^{85} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
912.3.b.a 912.b 228.b $2$ $24.850$ \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-57}) \) \(0\) \(-6\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}+9q^{9}+\beta q^{11}-19q^{19}-3\beta q^{23}+\cdots\)
912.3.b.b 912.b 228.b $2$ $24.850$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-6\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}+\zeta_{6}q^{7}+9q^{9}+\zeta_{6}q^{13}+(-13+\cdots)q^{19}+\cdots\)
912.3.b.c 912.b 228.b $2$ $24.850$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(6\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{3}-\zeta_{6}q^{7}+9q^{9}+\zeta_{6}q^{13}+(13+\cdots)q^{19}+\cdots\)
912.3.b.d 912.b 228.b $2$ $24.850$ \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-57}) \) \(0\) \(6\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{3}+9q^{9}-\beta q^{11}+19q^{19}+3\beta q^{23}+\cdots\)
912.3.b.e 912.b 228.b $4$ $24.850$ \(\Q(\sqrt{-11}, \sqrt{13})\) None \(0\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2-\beta _{1})q^{3}+(-2+4\beta _{1})q^{5}+(-2\beta _{2}+\cdots)q^{7}+\cdots\)
912.3.b.f 912.b 228.b $4$ $24.850$ \(\Q(\sqrt{-11}, \sqrt{13})\) None \(0\) \(10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+\beta _{1})q^{3}+(-2+4\beta _{1})q^{5}+(-2\beta _{2}+\cdots)q^{7}+\cdots\)
912.3.b.g 912.b 228.b $16$ $24.850$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{3}-\beta _{10}q^{5}-\beta _{4}q^{7}+(-3+\beta _{2}+\cdots)q^{9}+\cdots\)
912.3.b.h 912.b 228.b $48$ $24.850$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)