Properties

Label 420.2.k
Level $420$
Weight $2$
Character orbit 420.k
Rep. character $\chi_{420}(169,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 420.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(420, [\chi])\).

Total New Old
Modular forms 108 4 104
Cusp forms 84 4 80
Eisenstein series 24 0 24

Trace form

\( 4q - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{9} + 4q^{15} - 8q^{19} - 4q^{21} + 12q^{25} - 24q^{29} + 8q^{31} + 4q^{35} - 8q^{39} + 16q^{41} - 4q^{49} - 8q^{51} + 32q^{55} - 16q^{59} + 24q^{61} + 8q^{65} - 8q^{69} - 16q^{71} - 32q^{79} + 4q^{81} + 8q^{85} - 48q^{89} - 8q^{91} + 32q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(420, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
420.2.k.a \(2\) \(3.354\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{3}+(-2-i)q^{5}+iq^{7}-q^{9}+\cdots\)
420.2.k.b \(2\) \(3.354\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{3}+(2-i)q^{5}+iq^{7}-q^{9}+4q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(420, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(420, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)