Properties

Label 1296.2.c
Level $1296$
Weight $2$
Character orbit 1296.c
Rep. character $\chi_{1296}(1295,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $7$
Sturm bound $432$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1296.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(432\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1296, [\chi])\).

Total New Old
Modular forms 252 24 228
Cusp forms 180 24 156
Eisenstein series 72 0 72

Trace form

\( 24 q + O(q^{10}) \) \( 24 q - 24 q^{25} - 36 q^{37} - 24 q^{49} + 36 q^{61} - 36 q^{73} + 36 q^{85} + 36 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1296, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1296.2.c.a 1296.c 12.b $2$ $10.349$ \(\Q(\sqrt{-3}) \) None 144.2.s.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{5}-\zeta_{6}q^{7}-3q^{11}-5q^{13}+\cdots\)
1296.2.c.b 1296.c 12.b $2$ $10.349$ \(\Q(\sqrt{-3}) \) None 144.2.s.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\zeta_{6}q^{5}-2\zeta_{6}q^{7}-3q^{11}+4q^{13}+\cdots\)
1296.2.c.c 1296.c 12.b $2$ $10.349$ \(\Q(\sqrt{-3}) \) None 144.2.s.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{5}+\zeta_{6}q^{7}+3q^{11}-5q^{13}+\cdots\)
1296.2.c.d 1296.c 12.b $2$ $10.349$ \(\Q(\sqrt{-3}) \) None 144.2.s.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\zeta_{6}q^{5}+2\zeta_{6}q^{7}+3q^{11}+4q^{13}+\cdots\)
1296.2.c.e 1296.c 12.b $4$ $10.349$ \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-1}) \) 1296.2.c.e \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{5}+(-2+\beta _{3})q^{13}+(\beta _{1}-\beta _{2}+\cdots)q^{17}+\cdots\)
1296.2.c.f 1296.c 12.b $4$ $10.349$ \(\Q(\zeta_{12})\) None 144.2.s.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-\zeta_{12}^{3}q^{11}+\cdots\)
1296.2.c.g 1296.c 12.b $8$ $10.349$ \(\Q(\zeta_{24})\) None 1296.2.c.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{3}q^{5}-\zeta_{24}^{4}q^{7}-\zeta_{24}^{2}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1296, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)