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Properties

Label 392.3.ba
Level $392$
Weight $3$
Character orbit 392.ba
Rep. character $\chi_{392}(17,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $336$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 392.ba (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(392, [\chi])\).

Total New Old
Modular forms 1392 336 1056
Cusp forms 1296 336 960
Eisenstein series 96 0 96

Trace form

\( 336 q + 4 q^{7} - 148 q^{9} + O(q^{10}) \) \( 336 q + 4 q^{7} - 148 q^{9} - 4 q^{11} + 60 q^{15} + 24 q^{17} + 84 q^{19} + 52 q^{21} + 24 q^{23} - 128 q^{25} - 148 q^{29} - 156 q^{31} - 204 q^{33} - 296 q^{35} - 176 q^{37} - 204 q^{39} - 176 q^{43} + 52 q^{45} - 144 q^{47} + 80 q^{49} + 60 q^{51} + 60 q^{53} + 112 q^{55} + 152 q^{57} + 76 q^{59} - 56 q^{61} + 596 q^{63} - 84 q^{65} + 16 q^{67} + 168 q^{69} - 96 q^{71} + 156 q^{73} + 156 q^{75} + 240 q^{77} + 136 q^{79} + 1252 q^{81} + 784 q^{83} - 248 q^{85} + 520 q^{87} + 244 q^{89} + 356 q^{91} + 540 q^{93} - 8 q^{95} - 408 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(392, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
392.3.ba.a 392.ba 49.h $336$ $10.681$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{42}]$

Decomposition of \(S_{3}^{\mathrm{old}}(392, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(392, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)