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Properties

Label 36.6.b
Level $36$
Weight $6$
Character orbit 36.b
Rep. character $\chi_{36}(35,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $2$
Sturm bound $36$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 36.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(36, [\chi])\).

Total New Old
Modular forms 34 10 24
Cusp forms 26 10 16
Eisenstein series 8 0 8

Trace form

\( 10 q - 20 q^{4} + 668 q^{10} - 232 q^{13} - 2168 q^{16} + 9984 q^{22} - 3522 q^{25} - 23232 q^{28} + 47636 q^{34} - 1612 q^{37} - 76552 q^{40} + 84480 q^{46} + 38278 q^{49} - 80752 q^{52} + 82052 q^{58}+ \cdots + 551504 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(36, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.6.b.a 36.b 12.b $2$ $5.774$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) 36.6.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+4\beta q^{2}-2^{5}q^{4}-79\beta q^{5}-2^{7}\beta q^{8}+\cdots\)
36.6.b.b 36.b 12.b $8$ $5.774$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 36.6.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(6+\beta _{7})q^{4}+(6\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(36, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)