Properties

Label 12.3.c
Level $12$
Weight $3$
Character orbit 12.c
Rep. character $\chi_{12}(5,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 12.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(12, [\chi])\).

Total New Old
Modular forms 7 1 6
Cusp forms 1 1 0
Eisenstein series 6 0 6

Trace form

\( q - 3q^{3} + 2q^{7} + 9q^{9} + O(q^{10}) \) \( q - 3q^{3} + 2q^{7} + 9q^{9} - 22q^{13} + 26q^{19} - 6q^{21} + 25q^{25} - 27q^{27} - 46q^{31} + 26q^{37} + 66q^{39} - 22q^{43} - 45q^{49} - 78q^{57} + 74q^{61} + 18q^{63} + 122q^{67} - 46q^{73} - 75q^{75} - 142q^{79} + 81q^{81} - 44q^{91} + 138q^{93} + 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
12.3.c.a \(1\) \(0.327\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(2\) \(q-3q^{3}+2q^{7}+9q^{9}-22q^{13}+26q^{19}+\cdots\)