Properties

Label 108.3.d
Level $108$
Weight $3$
Character orbit 108.d
Rep. character $\chi_{108}(55,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $4$
Sturm bound $54$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(54\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(108, [\chi])\).

Total New Old
Modular forms 42 16 26
Cusp forms 30 16 14
Eisenstein series 12 0 12

Trace form

\( 16 q - 2 q^{4} + O(q^{10}) \) \( 16 q - 2 q^{4} + 14 q^{10} + 8 q^{13} + 10 q^{16} - 102 q^{22} + 72 q^{25} - 150 q^{28} - 40 q^{34} + 8 q^{37} + 170 q^{40} + 372 q^{46} - 176 q^{49} + 44 q^{52} - 340 q^{58} - 184 q^{61} - 326 q^{64} - 78 q^{70} - 64 q^{73} + 576 q^{76} + 596 q^{82} + 400 q^{85} + 342 q^{88} - 300 q^{94} + 128 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
108.3.d.a 108.d 4.b $2$ $2.943$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(14\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}+7q^{5}+\cdots\)
108.3.d.b 108.d 4.b $2$ $2.943$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}-7q^{5}+\cdots\)
108.3.d.c 108.d 4.b $4$ $2.943$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2})q^{2}+(3+\beta _{3})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
108.3.d.d 108.d 4.b $8$ $2.943$ 8.0.207360000.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-1+\beta _{5})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)