Properties

Label 684.3.y
Level $684$
Weight $3$
Character orbit 684.y
Rep. character $\chi_{684}(145,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $8$
Sturm bound $360$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.y (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(360\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(684, [\chi])\).

Total New Old
Modular forms 504 32 472
Cusp forms 456 32 424
Eisenstein series 48 0 48

Trace form

\( 32 q - q^{5} + 4 q^{7} + O(q^{10}) \) \( 32 q - q^{5} + 4 q^{7} + 14 q^{11} + 21 q^{13} - 19 q^{17} - 13 q^{19} + 17 q^{23} - 33 q^{25} - 51 q^{29} - 14 q^{35} + 54 q^{41} - 77 q^{43} - 79 q^{47} + 120 q^{49} - 33 q^{53} - 46 q^{55} - 30 q^{59} + 43 q^{61} - 12 q^{67} + 243 q^{71} + 16 q^{73} - 116 q^{77} + 63 q^{79} + 74 q^{83} + 101 q^{85} + 219 q^{89} - 102 q^{91} + 335 q^{95} + 216 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
684.3.y.a $2$ $18.638$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-2\) \(q+(-2+2\zeta_{6})q^{5}-q^{7}-2^{4}q^{11}+(18+\cdots)q^{13}+\cdots\)
684.3.y.b $2$ $18.638$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(22\) \(q+(-2+2\zeta_{6})q^{5}+11q^{7}+8q^{11}+\cdots\)
684.3.y.c $2$ $18.638$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-22\) \(q-11q^{7}+(30-15\zeta_{6})q^{13}+(-21+\cdots)q^{19}+\cdots\)
684.3.y.d $2$ $18.638$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(26\) \(q+13q^{7}+(14-7\zeta_{6})q^{13}+(-5-2^{4}\zeta_{6})q^{19}+\cdots\)
684.3.y.e $2$ $18.638$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(6\) \(-10\) \(q+(6-6\zeta_{6})q^{5}-5q^{7}+(-22+11\zeta_{6})q^{13}+\cdots\)
684.3.y.f $6$ $18.638$ 6.0.954288.1 None \(0\) \(0\) \(-4\) \(10\) \(q+(-\beta _{1}-2\beta _{2}+\beta _{4}-\beta _{5})q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
684.3.y.g $8$ $18.638$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(-8\) \(q+(\beta _{1}-\beta _{5})q^{5}+(-1+\beta _{3})q^{7}-\beta _{4}q^{11}+\cdots\)
684.3.y.h $8$ $18.638$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(1\) \(-12\) \(q+\beta _{5}q^{5}+(-2+\beta _{1})q^{7}+(1-\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(684, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)