Properties

Label 48.3.e
Level $48$
Weight $3$
Character orbit 48.e
Rep. character $\chi_{48}(17,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 48.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(48, [\chi])\).

Total New Old
Modular forms 22 5 17
Cusp forms 10 3 7
Eisenstein series 12 2 10

Trace form

\( 3q + q^{3} + 10q^{7} - 5q^{9} + O(q^{10}) \) \( 3q + q^{3} + 10q^{7} - 5q^{9} - 2q^{13} - 32q^{15} - 30q^{19} - 18q^{21} + 11q^{25} + 73q^{27} + 90q^{31} + 32q^{33} + 14q^{37} - 86q^{39} - 142q^{43} + 64q^{45} - 71q^{49} + 128q^{51} + 64q^{55} - 74q^{57} - 98q^{61} - 102q^{63} - 126q^{67} - 64q^{69} + 118q^{73} + 89q^{75} + 122q^{79} + 115q^{81} + 256q^{85} - 96q^{87} + 164q^{91} + 94q^{93} - 186q^{97} - 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
48.3.e.a \(1\) \(1.308\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-2\) \(q+3q^{3}-2q^{7}+9q^{9}-22q^{13}-26q^{19}+\cdots\)
48.3.e.b \(2\) \(1.308\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(12\) \(q+(-1+\beta )q^{3}+2\beta q^{5}+6q^{7}+(-7+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)