Properties

Label 882.4.g
Level $882$
Weight $4$
Character orbit 882.g
Rep. character $\chi_{882}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $100$
Newform subspaces $37$
Sturm bound $672$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 37 \)
Sturm bound: \(672\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(882, [\chi])\).

Total New Old
Modular forms 1072 100 972
Cusp forms 944 100 844
Eisenstein series 128 0 128

Trace form

\( 100 q - 200 q^{4} + 18 q^{5} + O(q^{10}) \) \( 100 q - 200 q^{4} + 18 q^{5} - 8 q^{10} + 2 q^{11} + 192 q^{13} - 800 q^{16} + 150 q^{17} - 46 q^{19} - 144 q^{20} - 400 q^{22} - 350 q^{23} - 1460 q^{25} + 120 q^{26} + 784 q^{29} + 138 q^{31} + 512 q^{34} - 874 q^{37} + 192 q^{38} - 32 q^{40} - 2016 q^{41} - 896 q^{43} + 8 q^{44} - 136 q^{46} - 102 q^{47} + 736 q^{50} - 384 q^{52} + 2546 q^{53} + 1916 q^{55} + 552 q^{58} - 90 q^{59} + 294 q^{61} - 3744 q^{62} + 6400 q^{64} - 2124 q^{65} - 310 q^{67} + 600 q^{68} + 2688 q^{71} - 1142 q^{73} - 440 q^{74} + 368 q^{76} + 730 q^{79} + 288 q^{80} - 1200 q^{82} - 2568 q^{83} + 9476 q^{85} + 1296 q^{86} + 800 q^{88} + 2754 q^{89} + 2800 q^{92} + 216 q^{94} + 3122 q^{95} + 160 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
882.4.g.a 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-22\zeta_{6}q^{5}+\cdots\)
882.4.g.b 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-14\zeta_{6}q^{5}+\cdots\)
882.4.g.c 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-8\zeta_{6}q^{5}+\cdots\)
882.4.g.d 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-7\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-7\zeta_{6}q^{5}+\cdots\)
882.4.g.e 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots\)
882.4.g.f 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots\)
882.4.g.g 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\)
882.4.g.h 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\)
882.4.g.i 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\)
882.4.g.j 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+8\zeta_{6}q^{5}+\cdots\)
882.4.g.k 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(14\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+14\zeta_{6}q^{5}+\cdots\)
882.4.g.l 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(15\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+15\zeta_{6}q^{5}+\cdots\)
882.4.g.m 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(22\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+22\zeta_{6}q^{5}+\cdots\)
882.4.g.n 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-22\zeta_{6}q^{5}+\cdots\)
882.4.g.o 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-18\zeta_{6}q^{5}+\cdots\)
882.4.g.p 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-12\zeta_{6}q^{5}+\cdots\)
882.4.g.q 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots\)
882.4.g.r 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
882.4.g.s 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
882.4.g.t 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\)
882.4.g.u 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(9\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+9\zeta_{6}q^{5}+\cdots\)
882.4.g.v 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+12\zeta_{6}q^{5}+\cdots\)
882.4.g.w 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(18\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+18\zeta_{6}q^{5}+\cdots\)
882.4.g.x 882.g 7.c $2$ $52.040$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(22\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+22\zeta_{6}q^{5}+\cdots\)
882.4.g.y 882.g 7.c $4$ $52.040$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-4\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+(-6-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.z 882.g 7.c $4$ $52.040$ \(\Q(\sqrt{-3}, \sqrt{193})\) None \(-4\) \(0\) \(-7\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.ba 882.g 7.c $4$ $52.040$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+14\beta _{1}q^{5}+\cdots\)
882.4.g.bb 882.g 7.c $4$ $52.040$ \(\Q(\sqrt{-3}, \sqrt{58})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
882.4.g.bc 882.g 7.c $4$ $52.040$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+5\beta _{1}q^{5}+\cdots\)
882.4.g.bd 882.g 7.c $4$ $52.040$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-4\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+(6+\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.be 882.g 7.c $4$ $52.040$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.bf 882.g 7.c $4$ $52.040$ \(\Q(\sqrt{-3}, \sqrt{1345})\) None \(4\) \(0\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.bg 882.g 7.c $4$ $52.040$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+5\beta _{1}q^{5}+\cdots\)
882.4.g.bh 882.g 7.c $4$ $52.040$ \(\Q(\sqrt{-3}, \sqrt{58})\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots\)
882.4.g.bi 882.g 7.c $4$ $52.040$ \(\Q(\sqrt{-3}, \sqrt{22})\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots\)
882.4.g.bj 882.g 7.c $4$ $52.040$ \(\Q(\sqrt{-3}, \sqrt{193})\) None \(4\) \(0\) \(7\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.bk 882.g 7.c $4$ $52.040$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)