Properties

Label 108.3.c
Level $108$
Weight $3$
Character orbit 108.c
Rep. character $\chi_{108}(53,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $54$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 45 3 42
Cusp forms 27 3 24
Eisenstein series 18 0 18

Trace form

\( 3 q - 3 q^{7} + O(q^{10}) \) \( 3 q - 3 q^{7} + 51 q^{13} - 21 q^{19} - 87 q^{25} + 24 q^{31} + 15 q^{37} - 66 q^{43} + 72 q^{49} - 162 q^{55} + 87 q^{61} + 15 q^{67} + 321 q^{73} + 231 q^{79} - 324 q^{85} + 57 q^{91} - 147 q^{97} + O(q^{100}) \)

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.c.a 108.c 3.b $1$ $2.943$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(11\) $\mathrm{U}(1)[D_{2}]$ \(q+11q^{7}+23q^{13}-37q^{19}+5^{2}q^{25}+\cdots\)
108.3.c.b 108.c 3.b $2$ $2.943$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}-7q^{7}+iq^{11}+14q^{13}+2iq^{17}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)