Properties

Label 12.3.c
Level 12
Weight 3
Character orbit c
Rep. character \(\chi_{12}(5,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(12, [\chi])\) into irreducible Hecke orbits

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