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Properties

Label 308.2.w
Level $308$
Weight $2$
Character orbit 308.w
Rep. character $\chi_{308}(13,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $32$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 308.w (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(308, [\chi])\).

Total New Old
Modular forms 216 32 184
Cusp forms 168 32 136
Eisenstein series 48 0 48

Trace form

\( 32 q - 5 q^{7} + 14 q^{9} + O(q^{10}) \) \( 32 q - 5 q^{7} + 14 q^{9} - 4 q^{11} - 6 q^{15} + 4 q^{23} + 32 q^{25} - 20 q^{29} + 15 q^{35} - 28 q^{37} - 20 q^{39} - 15 q^{49} + 60 q^{51} - 56 q^{53} + 80 q^{57} - 80 q^{63} - 88 q^{67} + 32 q^{71} - 37 q^{77} - 30 q^{79} - 66 q^{81} + 10 q^{85} - 49 q^{91} - 22 q^{93} - 50 q^{95} + 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(308, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
308.2.w.a 308.w 77.l $32$ $2.459$ None \(0\) \(0\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(308, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(308, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)