Properties

Label 240.3.c
Level $240$
Weight $3$
Character orbit 240.c
Rep. character $\chi_{240}(209,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $5$
Sturm bound $144$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 240.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(144\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(240, [\chi])\).

Total New Old
Modular forms 108 26 82
Cusp forms 84 22 62
Eisenstein series 24 4 20

Trace form

\( 22q - 2q^{9} + O(q^{10}) \) \( 22q - 2q^{9} - 14q^{15} + 20q^{19} + 8q^{21} - 10q^{25} + 36q^{31} + 32q^{39} + 24q^{45} - 154q^{49} + 116q^{51} - 64q^{55} + 140q^{61} + 36q^{69} - 192q^{75} - 28q^{79} - 154q^{81} + 44q^{85} - 384q^{91} - 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(240, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
240.3.c.a \(1\) \(6.540\) \(\Q\) \(\Q(\sqrt{-15}) \) \(0\) \(-3\) \(-5\) \(0\) \(q-3q^{3}-5q^{5}+9q^{9}+15q^{15}+14q^{17}+\cdots\)
240.3.c.b \(1\) \(6.540\) \(\Q\) \(\Q(\sqrt{-15}) \) \(0\) \(3\) \(5\) \(0\) \(q+3q^{3}+5q^{5}+9q^{9}+15q^{15}-14q^{17}+\cdots\)
240.3.c.c \(4\) \(6.540\) \(\Q(\sqrt{2}, \sqrt{-17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(2\beta _{2}+\beta _{3})q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
240.3.c.d \(4\) \(6.540\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots\)
240.3.c.e \(12\) \(6.540\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{7}q^{5}-\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)