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Properties

Label 308.2.j
Level $308$
Weight $2$
Character orbit 308.j
Rep. character $\chi_{308}(113,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $24$
Newform subspaces $3$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 308.j (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 3 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 216 24 192
Cusp forms 168 24 144
Eisenstein series 48 0 48

Trace form

\( 24 q + 2 q^{3} - 2 q^{5} + 2 q^{9} + O(q^{10}) \) \( 24 q + 2 q^{3} - 2 q^{5} + 2 q^{9} + 8 q^{11} - 2 q^{13} - 26 q^{19} - 20 q^{21} - 12 q^{23} - 12 q^{25} - 28 q^{27} + 26 q^{29} + 22 q^{31} - 8 q^{33} + 4 q^{35} + 14 q^{37} + 18 q^{39} + 20 q^{43} + 40 q^{45} - 6 q^{49} + 6 q^{51} + 18 q^{53} + 6 q^{55} + 26 q^{57} - 18 q^{59} - 48 q^{61} - 64 q^{65} + 24 q^{67} - 54 q^{69} + 30 q^{71} - 32 q^{73} - 26 q^{75} - 4 q^{77} - 28 q^{79} - 2 q^{81} + 36 q^{83} - 20 q^{85} - 12 q^{87} + 24 q^{89} + 18 q^{91} - 8 q^{93} - 20 q^{95} - 6 q^{97} - 96 q^{99} + O(q^{100}) \)

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.j.a 308.j 11.c $4$ $2.459$ \(\Q(\zeta_{10})\) None \(0\) \(4\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2\zeta_{10}+2\zeta_{10}^{3})q^{3}-2\zeta_{10}q^{5}+\zeta_{10}^{3}q^{7}+\cdots\)
308.2.j.b 308.j 11.c $8$ $2.459$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-8\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-2-2\beta _{2}-\beta _{3}-\beta _{6})q^{3}+\beta _{7}q^{5}+\cdots\)
308.2.j.c 308.j 11.c $12$ $2.459$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(6\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{8}-\beta _{9}+\beta _{11})q^{3}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(308, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)