Properties

Label 304.3.e
Level $304$
Weight $3$
Character orbit 304.e
Rep. character $\chi_{304}(113,\cdot)$
Character field $\Q$
Dimension $19$
Newform subspaces $7$
Sturm bound $120$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 304.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(120\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(304, [\chi])\).

Total New Old
Modular forms 86 21 65
Cusp forms 74 19 55
Eisenstein series 12 2 10

Trace form

\( 19 q - 2 q^{5} - 14 q^{7} - 61 q^{9} + O(q^{10}) \) \( 19 q - 2 q^{5} - 14 q^{7} - 61 q^{9} + 2 q^{11} - 26 q^{17} + 33 q^{19} + 26 q^{23} + 73 q^{25} - 44 q^{35} + 32 q^{39} - 126 q^{43} - 34 q^{45} - 94 q^{47} + 121 q^{49} - 116 q^{55} - 40 q^{57} - 82 q^{61} + 418 q^{63} + 54 q^{73} - 180 q^{77} + 403 q^{81} + 82 q^{83} - 244 q^{85} - 528 q^{87} - 80 q^{93} + 210 q^{95} + 82 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
304.3.e.a \(1\) \(8.283\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-9\) \(5\) \(q-9q^{5}+5q^{7}+9q^{9}-3q^{11}+15q^{17}+\cdots\)
304.3.e.b \(2\) \(8.283\) \(\Q(\sqrt{-29}) \) None \(0\) \(0\) \(-8\) \(2\) \(q+\beta q^{3}-4q^{5}+q^{7}-20q^{9}-14q^{11}+\cdots\)
304.3.e.c \(2\) \(8.283\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(-2\) \(-10\) \(q+\beta q^{3}-q^{5}-5q^{7}+q^{9}-5q^{11}+\cdots\)
304.3.e.d \(2\) \(8.283\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(8\) \(10\) \(q+\beta q^{3}+4q^{5}+5q^{7}-4q^{9}+10q^{11}+\cdots\)
304.3.e.e \(2\) \(8.283\) \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(9\) \(-5\) \(q+(5-\beta )q^{5}+(-1-3\beta )q^{7}+9q^{9}+\cdots\)
304.3.e.f \(2\) \(8.283\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(14\) \(-22\) \(q+\beta q^{3}+7q^{5}-11q^{7}-23q^{9}-3q^{11}+\cdots\)
304.3.e.g \(8\) \(8.283\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(-14\) \(6\) \(q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(1-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

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