Properties

Label 1296.2.i
Level $1296$
Weight $2$
Character orbit 1296.i
Rep. character $\chi_{1296}(433,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $46$
Newform subspaces $20$
Sturm bound $432$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1296.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 20 \)
Sturm bound: \(432\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 504 50 454
Cusp forms 360 46 314
Eisenstein series 144 4 140

Trace form

\( 46 q - 2 q^{7} + O(q^{10}) \) \( 46 q - 2 q^{7} + 2 q^{13} + 4 q^{19} - 17 q^{25} - 32 q^{31} - 4 q^{37} - 32 q^{43} - 15 q^{49} + 24 q^{55} + 2 q^{61} - 2 q^{67} + 20 q^{73} - 2 q^{79} + 12 q^{85} + 92 q^{91} - 10 q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1296.2.i.a \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-4\) \(-3\) \(q-4\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
1296.2.i.b \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-4\) \(q-3\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\zeta_{6}q^{13}+\cdots\)
1296.2.i.c \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-1\) \(q-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1296.2.i.d \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(2\) \(q-3\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
1296.2.i.e \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots\)
1296.2.i.f \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+5\zeta_{6}q^{13}+\cdots\)
1296.2.i.g \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(3\) \(q-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
1296.2.i.h \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) \(q+(-4+4\zeta_{6})q^{7}-2\zeta_{6}q^{13}-8q^{19}+\cdots\)
1296.2.i.i \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) \(q+(-1+\zeta_{6})q^{7}-5\zeta_{6}q^{13}+7q^{19}+\cdots\)
1296.2.i.j \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) \(q+(5-5\zeta_{6})q^{7}+7\zeta_{6}q^{13}+q^{19}+(5+\cdots)q^{25}+\cdots\)
1296.2.i.k \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+5\zeta_{6}q^{13}+\cdots\)
1296.2.i.l \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(3\) \(q+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots\)
1296.2.i.m \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots\)
1296.2.i.n \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-4\) \(q+3\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\zeta_{6}q^{13}+\cdots\)
1296.2.i.o \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-1\) \(q+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
1296.2.i.p \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(2\) \(q+3\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
1296.2.i.q \(2\) \(10.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(4\) \(-3\) \(q+4\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
1296.2.i.r \(4\) \(10.349\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2\zeta_{12}+\zeta_{12}^{2})q^{5}+(2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{7}+\cdots\)
1296.2.i.s \(4\) \(10.349\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{12}^{2}q^{5}+(2-2\zeta_{12})q^{7}+(-2\zeta_{12}^{2}+\cdots)q^{11}+\cdots\)
1296.2.i.t \(4\) \(10.349\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) \(q+(2-2\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+2\zeta_{12}^{2}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1296, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)