Properties

Label 12.5.c
Level 12
Weight 5
Character orbit c
Rep. character \(\chi_{12}(5,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 12.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(12, [\chi])\).

Total New Old
Modular forms 11 1 10
Cusp forms 5 1 4
Eisenstein series 6 0 6

Trace form

\(q \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 94q^{7} \) \(\mathstrut +\mathstrut 81q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 94q^{7} \) \(\mathstrut +\mathstrut 81q^{9} \) \(\mathstrut +\mathstrut 146q^{13} \) \(\mathstrut -\mathstrut 46q^{19} \) \(\mathstrut -\mathstrut 846q^{21} \) \(\mathstrut +\mathstrut 625q^{25} \) \(\mathstrut +\mathstrut 729q^{27} \) \(\mathstrut +\mathstrut 194q^{31} \) \(\mathstrut -\mathstrut 2062q^{37} \) \(\mathstrut +\mathstrut 1314q^{39} \) \(\mathstrut -\mathstrut 3214q^{43} \) \(\mathstrut +\mathstrut 6435q^{49} \) \(\mathstrut -\mathstrut 414q^{57} \) \(\mathstrut -\mathstrut 1966q^{61} \) \(\mathstrut -\mathstrut 7614q^{63} \) \(\mathstrut +\mathstrut 5906q^{67} \) \(\mathstrut -\mathstrut 8542q^{73} \) \(\mathstrut +\mathstrut 5625q^{75} \) \(\mathstrut +\mathstrut 7682q^{79} \) \(\mathstrut +\mathstrut 6561q^{81} \) \(\mathstrut -\mathstrut 13724q^{91} \) \(\mathstrut +\mathstrut 1746q^{93} \) \(\mathstrut -\mathstrut 18814q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(12, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
12.5.c.a \(1\) \(1.240\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(9\) \(0\) \(-94\) \(q+9q^{3}-94q^{7}+3^{4}q^{9}+146q^{13}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)