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Properties

Label 456.3.w
Level $456$
Weight $3$
Character orbit 456.w
Rep. character $\chi_{456}(145,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $2$
Sturm bound $240$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 456.w (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(456, [\chi])\).

Total New Old
Modular forms 336 40 296
Cusp forms 304 40 264
Eisenstein series 32 0 32

Trace form

\( 40 q + 16 q^{7} + 60 q^{9} + O(q^{10}) \) \( 40 q + 16 q^{7} + 60 q^{9} - 16 q^{11} + 12 q^{13} + 16 q^{17} + 8 q^{19} - 36 q^{21} - 64 q^{23} - 116 q^{25} - 96 q^{29} + 40 q^{35} - 48 q^{39} - 24 q^{41} + 32 q^{43} + 24 q^{47} + 688 q^{49} - 72 q^{53} + 192 q^{55} - 84 q^{57} + 240 q^{59} + 116 q^{61} + 24 q^{63} + 384 q^{67} + 72 q^{71} + 100 q^{73} - 160 q^{77} - 288 q^{79} - 180 q^{81} - 224 q^{83} + 16 q^{85} - 624 q^{87} - 432 q^{89} - 288 q^{91} - 228 q^{93} + 320 q^{95} - 408 q^{97} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(456, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
456.3.w.a 456.w 19.d $20$ $12.425$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(-30\) \(0\) \(20\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{3})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{15}+\cdots)q^{7}+\cdots\)
456.3.w.b 456.w 19.d $20$ $12.425$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(30\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{3})q^{3}+(-\beta _{2}-\beta _{13})q^{5}-\beta _{5}q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(456, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(456, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)