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Properties

Label 40.3.e
Level $40$
Weight $3$
Character orbit 40.e
Rep. character $\chi_{40}(19,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $3$
Sturm bound $18$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 40.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(18\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

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

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

Trace form

\( 10 q - 4 q^{4} + 12 q^{6} - 22 q^{9} - 4 q^{11} - 44 q^{14} - 40 q^{16} + 28 q^{19} + 20 q^{20} + 112 q^{24} + 10 q^{25} - 56 q^{26} + 100 q^{30} + 152 q^{34} - 100 q^{35} + 52 q^{36} - 160 q^{40} + 36 q^{41}+ \cdots - 164 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
40.3.e.a 40.e 40.e $1$ $1.090$ \(\Q\) \(\Q(\sqrt{-10}) \) 40.3.e.a \(-2\) \(0\) \(5\) \(6\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+4q^{4}+5q^{5}+6q^{7}-8q^{8}+\cdots\)
40.3.e.b 40.e 40.e $1$ $1.090$ \(\Q\) \(\Q(\sqrt{-10}) \) 40.3.e.a \(2\) \(0\) \(-5\) \(-6\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+4q^{4}-5q^{5}-6q^{7}+8q^{8}+\cdots\)
40.3.e.c 40.e 40.e $8$ $1.090$ 8.0.\(\cdots\).2 None 40.3.e.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{7}q^{3}+(-2-\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots\)