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Properties

Label 40.3.l
Level $40$
Weight $3$
Character orbit 40.l
Rep. character $\chi_{40}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $6$
Newform subspaces $2$
Sturm bound $18$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 40.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(40, [\chi])\).

Total New Old
Modular forms 32 6 26
Cusp forms 16 6 10
Eisenstein series 16 0 16

Trace form

\( 6 q + 4 q^{5} + 8 q^{7} + O(q^{10}) \) \( 6 q + 4 q^{5} + 8 q^{7} - 8 q^{11} - 38 q^{13} - 72 q^{15} - 14 q^{17} + 56 q^{21} + 96 q^{23} + 50 q^{25} + 120 q^{27} - 16 q^{31} - 120 q^{33} - 72 q^{35} - 82 q^{37} + 56 q^{41} + 48 q^{43} + 154 q^{45} - 128 q^{47} - 240 q^{51} - 66 q^{53} - 88 q^{55} - 80 q^{57} - 24 q^{61} + 128 q^{63} + 134 q^{65} + 224 q^{67} + 272 q^{71} + 166 q^{73} + 264 q^{75} + 72 q^{77} - 46 q^{81} - 184 q^{83} - 198 q^{85} - 320 q^{87} - 352 q^{91} + 120 q^{93} - 104 q^{95} + 38 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(40, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
40.3.l.a 40.l 5.c $2$ $1.090$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(10\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+5q^{5}+(-3-3i)q^{7}+\cdots\)
40.3.l.b 40.l 5.c $4$ $1.090$ \(\Q(i, \sqrt{41})\) None \(0\) \(-2\) \(-6\) \(14\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{2})q^{3}+(-1-2\beta _{1}+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(40, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(40, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)