Properties

Label 304.5.e
Level $304$
Weight $5$
Character orbit 304.e
Rep. character $\chi_{304}(113,\cdot)$
Character field $\Q$
Dimension $39$
Newform subspaces $6$
Sturm bound $200$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 304.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(200\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 166 41 125
Cusp forms 154 39 115
Eisenstein series 12 2 10

Trace form

\( 39q - 2q^{5} - 30q^{7} - 889q^{9} + O(q^{10}) \) \( 39q - 2q^{5} - 30q^{7} - 889q^{9} + 2q^{11} - 50q^{17} + 65q^{19} - 718q^{23} + 4373q^{25} + 4132q^{35} + 3008q^{39} + 2818q^{43} - 1090q^{45} + 2882q^{47} + 9845q^{49} + 7828q^{55} + 1136q^{57} + 7902q^{61} - 7742q^{63} - 274q^{73} - 484q^{77} + 5671q^{81} + 6434q^{83} + 15260q^{85} + 33120q^{87} + 14560q^{93} + 15458q^{95} + 24610q^{99} + O(q^{100}) \)

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.e.a \(1\) \(31.424\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(31\) \(73\) \(q+31q^{5}+73q^{7}+3^{4}q^{9}+233q^{11}+\cdots\)
304.5.e.b \(2\) \(31.424\) \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-31\) \(-73\) \(q+(-17-3\beta )q^{5}+(-39-5\beta )q^{7}+\cdots\)
304.5.e.c \(4\) \(31.424\) 4.0.12107488.1 None \(0\) \(0\) \(-42\) \(-136\) \(q-\beta _{2}q^{3}+(-10-\beta _{3})q^{5}+(-31-6\beta _{3})q^{7}+\cdots\)
304.5.e.d \(4\) \(31.424\) \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(0\) \(0\) \(22\) \(-24\) \(q+\beta _{1}q^{3}+(6-\beta _{2})q^{5}+(-7+2\beta _{2}+\cdots)q^{7}+\cdots\)
304.5.e.e \(8\) \(31.424\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(18\) \(162\) \(q-\beta _{1}q^{3}+(2-\beta _{5})q^{5}+(20-\beta _{4})q^{7}+\cdots\)
304.5.e.f \(20\) \(31.424\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(-32\) \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-2+\beta _{5})q^{7}+(-19+\cdots)q^{9}+\cdots\)

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

\( S_{5}^{\mathrm{old}}(304, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)