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Properties

Label 296.2.ba
Level $296$
Weight $2$
Character orbit 296.ba
Rep. character $\chi_{296}(25,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $60$
Newform subspaces $1$
Sturm bound $76$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 296 = 2^{3} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 296.ba (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(76\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(296, [\chi])\).

Total New Old
Modular forms 252 60 192
Cusp forms 204 60 144
Eisenstein series 48 0 48

Trace form

\( 60 q - 6 q^{5} + 6 q^{7} + O(q^{10}) \) \( 60 q - 6 q^{5} + 6 q^{7} - 18 q^{11} - 12 q^{13} + 18 q^{15} + 6 q^{17} + 6 q^{19} + 6 q^{21} + 12 q^{25} - 42 q^{27} + 6 q^{35} - 18 q^{37} + 18 q^{39} + 12 q^{41} + 18 q^{49} + 18 q^{53} - 12 q^{55} + 6 q^{57} - 60 q^{61} + 6 q^{63} - 60 q^{65} - 6 q^{67} - 60 q^{69} - 30 q^{71} + 12 q^{73} - 144 q^{75} + 24 q^{77} + 30 q^{79} - 72 q^{81} - 24 q^{83} - 24 q^{85} + 24 q^{87} - 18 q^{89} - 84 q^{91} - 48 q^{93} - 18 q^{95} + 36 q^{97} + 84 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(296, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
296.2.ba.a 296.ba 37.h $60$ $2.364$ None \(0\) \(0\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(296, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(296, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 2}\)