Properties

Label 60.4.d
Level $60$
Weight $4$
Character orbit 60.d
Rep. character $\chi_{60}(49,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 60.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(60, [\chi])\).

Total New Old
Modular forms 42 2 40
Cusp forms 30 2 28
Eisenstein series 12 0 12

Trace form

\( 2 q - 20 q^{5} - 18 q^{9} + O(q^{10}) \) \( 2 q - 20 q^{5} - 18 q^{9} - 28 q^{11} - 30 q^{15} + 240 q^{19} - 132 q^{21} + 150 q^{25} - 192 q^{29} + 368 q^{31} - 220 q^{35} - 180 q^{39} + 260 q^{41} + 180 q^{45} - 282 q^{49} - 372 q^{51} + 280 q^{55} - 532 q^{59} - 1676 q^{61} - 300 q^{65} + 1128 q^{69} + 2040 q^{71} + 600 q^{75} + 96 q^{79} + 162 q^{81} - 620 q^{85} + 1300 q^{89} - 1320 q^{91} - 2400 q^{95} + 252 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(60, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
60.4.d.a $2$ $3.540$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-20\) \(0\) \(q+3iq^{3}+(-10+5i)q^{5}+22iq^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(60, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)