Properties

Label 308.2.i
Level $308$
Weight $2$
Character orbit 308.i
Rep. character $\chi_{308}(177,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $2$
Sturm bound $96$
Trace bound $3$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 108 12 96
Cusp forms 84 12 72
Eisenstein series 24 0 24

Trace form

\( 12 q + 2 q^{3} + 4 q^{5} + 6 q^{7} - 8 q^{9} + O(q^{10}) \) \( 12 q + 2 q^{3} + 4 q^{5} + 6 q^{7} - 8 q^{9} - 28 q^{15} + 6 q^{17} - 2 q^{19} - 18 q^{21} + 4 q^{23} - 6 q^{25} + 32 q^{27} + 8 q^{29} - 10 q^{31} + 4 q^{33} - 26 q^{35} - 12 q^{37} - 10 q^{39} + 24 q^{41} + 36 q^{43} + 14 q^{45} - 10 q^{47} - 12 q^{51} + 6 q^{53} + 8 q^{57} + 4 q^{59} + 4 q^{61} + 54 q^{63} + 34 q^{65} - 60 q^{69} - 20 q^{71} - 34 q^{73} - 10 q^{75} - 2 q^{77} - 12 q^{79} - 6 q^{81} - 44 q^{83} - 32 q^{85} + 42 q^{87} + 30 q^{89} - 54 q^{91} - 20 q^{93} + 16 q^{95} + 28 q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
308.2.i.a $6$ $2.459$ 6.0.309123.1 None \(0\) \(-1\) \(2\) \(4\) \(q-\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{5}+\cdots\)
308.2.i.b $6$ $2.459$ 6.0.1783323.2 None \(0\) \(3\) \(2\) \(2\) \(q+(1-\beta _{4}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(308, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)