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Properties

Label 108.2.b
Level $108$
Weight $2$
Character orbit 108.b
Rep. character $\chi_{108}(107,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $36$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 108.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(108, [\chi])\).

Total New Old
Modular forms 24 8 16
Cusp forms 12 8 4
Eisenstein series 12 0 12

Trace form

\( 8 q + 2 q^{4} - 2 q^{10} + 4 q^{13} - 22 q^{16} - 18 q^{22} - 12 q^{25} + 18 q^{28} + 28 q^{34} - 20 q^{37} + 22 q^{40} - 16 q^{49} - 8 q^{52} + 4 q^{58} + 28 q^{61} - 10 q^{64} + 54 q^{70} + 16 q^{73}+ \cdots - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
108.2.b.a 108.b 12.b $4$ $0.862$ \(\Q(\sqrt{3}, \sqrt{-5})\) None 108.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
108.2.b.b 108.b 12.b $4$ $0.862$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 108.2.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(108, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)