Properties

Label 36.3.d
Level $36$
Weight $3$
Character orbit 36.d
Rep. character $\chi_{36}(19,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $18$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 36.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(18\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(36, [\chi])\).

Total New Old
Modular forms 16 6 10
Cusp forms 8 4 4
Eisenstein series 8 2 6

Trace form

\( 4 q + 2 q^{2} + 4 q^{4} + 4 q^{5} - 16 q^{8} - 28 q^{10} - 16 q^{13} + 24 q^{14} + 16 q^{16} - 20 q^{17} - 8 q^{20} + 24 q^{22} + 36 q^{25} + 4 q^{26} + 48 q^{28} + 52 q^{29} + 32 q^{32} + 44 q^{34} - 88 q^{37}+ \cdots + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(36, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.3.d.a 36.d 4.b $1$ $0.981$ \(\Q\) \(\Q(\sqrt{-1}) \) 36.3.d.a \(-2\) \(0\) \(8\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+4q^{4}+8q^{5}-8q^{8}-2^{4}q^{10}+\cdots\)
36.3.d.b 36.d 4.b $1$ $0.981$ \(\Q\) \(\Q(\sqrt{-1}) \) 36.3.d.a \(2\) \(0\) \(-8\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+4q^{4}-8q^{5}+8q^{8}-2^{4}q^{10}+\cdots\)
36.3.d.c 36.d 4.b $2$ $0.981$ \(\Q(\sqrt{-3}) \) None 12.3.d.a \(2\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta+1)q^{2}+(2\beta-2)q^{4}+2 q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(36, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)