Properties

Label 1728.2.bc
Level $1728$
Weight $2$
Character orbit 1728.bc
Rep. character $\chi_{1728}(145,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $88$
Newform subspaces $5$
Sturm bound $576$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1728.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(576\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1728, [\chi])\).

Total New Old
Modular forms 1248 104 1144
Cusp forms 1056 88 968
Eisenstein series 192 16 176

Trace form

\( 88q + 2q^{5} + O(q^{10}) \) \( 88q + 2q^{5} - 2q^{11} - 2q^{13} + 16q^{17} + 8q^{19} + 2q^{29} + 4q^{31} - 28q^{35} - 8q^{37} + 2q^{43} - 44q^{47} + 16q^{49} + 8q^{53} + 10q^{59} - 2q^{61} + 4q^{65} + 2q^{67} + 30q^{77} + 4q^{79} - 22q^{83} - 12q^{85} + 36q^{91} + 60q^{95} - 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1728.2.bc.a \(4\) \(13.798\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(-6\) \(q+(-2\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+(-2-\zeta_{12}+\cdots)q^{7}+\cdots\)
1728.2.bc.b \(4\) \(13.798\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(12\) \(q+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+(4-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
1728.2.bc.c \(4\) \(13.798\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(-12\) \(q+(1+\zeta_{12}-\zeta_{12}^{3})q^{5}+(-4-\zeta_{12}+\cdots)q^{7}+\cdots\)
1728.2.bc.d \(4\) \(13.798\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(8\) \(6\) \(q+(2+2\zeta_{12}-2\zeta_{12}^{3})q^{5}+(2-\zeta_{12}+\cdots)q^{7}+\cdots\)
1728.2.bc.e \(72\) \(13.798\) None \(0\) \(0\) \(-4\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)