Properties

Label 304.5.d
Level $304$
Weight $5$
Character orbit 304.d
Rep. character $\chi_{304}(191,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $2$
Sturm bound $200$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 304.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(200\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(304, [\chi])\).

Total New Old
Modular forms 166 36 130
Cusp forms 154 36 118
Eisenstein series 12 0 12

Trace form

\( 36q - 72q^{5} - 972q^{9} + O(q^{10}) \) \( 36q - 72q^{5} - 972q^{9} - 360q^{13} + 360q^{17} - 1824q^{21} + 6204q^{25} + 5688q^{29} - 4320q^{33} - 4200q^{37} - 1080q^{41} + 7992q^{45} - 12828q^{49} + 2520q^{53} - 6600q^{61} + 7056q^{65} - 41472q^{69} + 12840q^{73} + 30384q^{77} + 33828q^{81} + 15360q^{85} - 15768q^{89} - 44640q^{93} - 4920q^{97} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
304.5.d.a \(12\) \(31.424\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-18\) \(0\) \(q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+\beta _{5}q^{7}+(-28+\cdots)q^{9}+\cdots\)
304.5.d.b \(24\) \(31.424\) None \(0\) \(0\) \(-54\) \(0\)

Decomposition of \(S_{5}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(304, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)