Properties

Label 480.2.f
Level $480$
Weight $2$
Character orbit 480.f
Rep. character $\chi_{480}(289,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $5$
Sturm bound $192$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 480.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(192\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(7\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(480, [\chi])\).

Total New Old
Modular forms 112 12 100
Cusp forms 80 12 68
Eisenstein series 32 0 32

Trace form

\( 12q - 4q^{5} - 12q^{9} + O(q^{10}) \) \( 12q - 4q^{5} - 12q^{9} - 20q^{25} + 8q^{29} + 40q^{41} + 4q^{45} - 12q^{49} - 8q^{61} + 12q^{81} - 64q^{85} - 40q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(480, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
480.2.f.a \(2\) \(3.833\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{3}+(-2+i)q^{5}-2iq^{7}-q^{9}+\cdots\)
480.2.f.b \(2\) \(3.833\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{3}+(-2-i)q^{5}-2iq^{7}-q^{9}+\cdots\)
480.2.f.c \(2\) \(3.833\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1+2i)q^{5}+4iq^{7}-q^{9}+\cdots\)
480.2.f.d \(2\) \(3.833\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1-2i)q^{5}+4iq^{7}-q^{9}+\cdots\)
480.2.f.e \(4\) \(3.833\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}-2\beta _{1}q^{7}-q^{9}-2\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(480, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(480, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)