LMFDB - Space of modular forms of level 882, weight 4, and Character 882.g

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

$ 100q - 200q^{4} + 18q^{5} + O(q^{10}) $

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

Display 100 coefficients 10 coefficients

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

Label	Dim.	$A$	Field	CM	Traces				$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	$q$-expansion
882.4.g.a	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$-2$	$0$	$-22$	$0$	$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-22\zeta_{6}q^{5}+\cdots$
882.4.g.b	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$-2$	$0$	$-14$	$0$	$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-14\zeta_{6}q^{5}+\cdots$
882.4.g.c	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$-2$	$0$	$-8$	$0$	$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-8\zeta_{6}q^{5}+\cdots$
882.4.g.d	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$-2$	$0$	$-7$	$0$	$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-7\zeta_{6}q^{5}+\cdots$
882.4.g.e	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$-2$	$0$	$-6$	$0$	$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots$
882.4.g.f	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$-2$	$0$	$-6$	$0$	$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots$
882.4.g.g	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$-2$	$0$	$6$	$0$	$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots$
882.4.g.h	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$-2$	$0$	$6$	$0$	$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots$
882.4.g.i	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$-2$	$0$	$6$	$0$	$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots$
882.4.g.j	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$-2$	$0$	$8$	$0$	$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+8\zeta_{6}q^{5}+\cdots$
882.4.g.k	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$-2$	$0$	$14$	$0$	$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+14\zeta_{6}q^{5}+\cdots$
882.4.g.l	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$-2$	$0$	$15$	$0$	$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+15\zeta_{6}q^{5}+\cdots$
882.4.g.m	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$-2$	$0$	$22$	$0$	$q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+22\zeta_{6}q^{5}+\cdots$
882.4.g.n	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$2$	$0$	$-22$	$0$	$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-22\zeta_{6}q^{5}+\cdots$
882.4.g.o	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$2$	$0$	$-18$	$0$	$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-18\zeta_{6}q^{5}+\cdots$
882.4.g.p	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$2$	$0$	$-12$	$0$	$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-12\zeta_{6}q^{5}+\cdots$
882.4.g.q	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$2$	$0$	$-6$	$0$	$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots$
882.4.g.r	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$2$	$0$	$-2$	$0$	$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots$
882.4.g.s	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$2$	$0$	$2$	$0$	$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots$
882.4.g.t	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$2$	$0$	$6$	$0$	$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots$
882.4.g.u	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$2$	$0$	$9$	$0$	$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+9\zeta_{6}q^{5}+\cdots$
882.4.g.v	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$2$	$0$	$12$	$0$	$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+12\zeta_{6}q^{5}+\cdots$
882.4.g.w	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$2$	$0$	$18$	$0$	$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+18\zeta_{6}q^{5}+\cdots$
882.4.g.x	$2$	$52.040$	$\Q(\sqrt{-3}) $	None	$2$	$0$	$22$	$0$	$q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+22\zeta_{6}q^{5}+\cdots$
882.4.g.y	$4$	$52.040$	$\Q(\sqrt{2}, \sqrt{-3})$	None	$-4$	$0$	$-12$	$0$	$q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+(-6-\beta _{1}+\cdots)q^{5}+\cdots$
882.4.g.z	$4$	$52.040$	$\Q(\sqrt{-3}, \sqrt{193})$	None	$-4$	$0$	$-7$	$0$	$q-2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
882.4.g.ba	$4$	$52.040$	$\Q(\sqrt{2}, \sqrt{-3})$	None	$-4$	$0$	$0$	$0$	$q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+14\beta _{1}q^{5}+\cdots$
882.4.g.bb	$4$	$52.040$	$\Q(\sqrt{-3}, \sqrt{58})$	None	$-4$	$0$	$0$	$0$	$q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots$
882.4.g.bc	$4$	$52.040$	$\Q(\sqrt{2}, \sqrt{-3})$	None	$-4$	$0$	$0$	$0$	$q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+5\beta _{1}q^{5}+\cdots$
882.4.g.bd	$4$	$52.040$	$\Q(\sqrt{2}, \sqrt{-3})$	None	$-4$	$0$	$12$	$0$	$q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+(6+\beta _{1}+\cdots)q^{5}+\cdots$
882.4.g.be	$4$	$52.040$	$\Q(\sqrt{2}, \sqrt{-3})$	None	$4$	$0$	$-12$	$0$	$q-2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
882.4.g.bf	$4$	$52.040$	$\Q(\sqrt{-3}, \sqrt{1345})$	None	$4$	$0$	$-5$	$0$	$q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
882.4.g.bg	$4$	$52.040$	$\Q(\sqrt{2}, \sqrt{-3})$	None	$4$	$0$	$0$	$0$	$q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+5\beta _{1}q^{5}+\cdots$
882.4.g.bh	$4$	$52.040$	$\Q(\sqrt{-3}, \sqrt{58})$	None	$4$	$0$	$0$	$0$	$q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots$
882.4.g.bi	$4$	$52.040$	$\Q(\sqrt{-3}, \sqrt{22})$	None	$4$	$0$	$0$	$0$	$q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots$
882.4.g.bj	$4$	$52.040$	$\Q(\sqrt{-3}, \sqrt{193})$	None	$4$	$0$	$7$	$0$	$q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
882.4.g.bk	$4$	$52.040$	$\Q(\sqrt{2}, \sqrt{-3})$	None	$4$	$0$	$12$	$0$	$q-2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$

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

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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 \(T_p\):			\(5\), \(11\), \(13\)

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
882.4.g.a	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(0\)	\(-22\)	\(0\)	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-22\zeta_{6}q^{5}+\cdots\)
882.4.g.b	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(0\)	\(-14\)	\(0\)	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-14\zeta_{6}q^{5}+\cdots\)
882.4.g.c	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(0\)	\(-8\)	\(0\)	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-8\zeta_{6}q^{5}+\cdots\)
882.4.g.d	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(0\)	\(-7\)	\(0\)	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-7\zeta_{6}q^{5}+\cdots\)
882.4.g.e	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(0\)	\(-6\)	\(0\)	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots\)
882.4.g.f	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(0\)	\(-6\)	\(0\)	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots\)
882.4.g.g	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(0\)	\(6\)	\(0\)	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\)
882.4.g.h	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(0\)	\(6\)	\(0\)	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\)
882.4.g.i	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(0\)	\(6\)	\(0\)	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\)
882.4.g.j	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(0\)	\(8\)	\(0\)	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+8\zeta_{6}q^{5}+\cdots\)
882.4.g.k	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(0\)	\(14\)	\(0\)	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+14\zeta_{6}q^{5}+\cdots\)
882.4.g.l	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(0\)	\(15\)	\(0\)	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+15\zeta_{6}q^{5}+\cdots\)
882.4.g.m	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(0\)	\(22\)	\(0\)	\(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+22\zeta_{6}q^{5}+\cdots\)
882.4.g.n	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(0\)	\(-22\)	\(0\)	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-22\zeta_{6}q^{5}+\cdots\)
882.4.g.o	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(0\)	\(-18\)	\(0\)	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-18\zeta_{6}q^{5}+\cdots\)
882.4.g.p	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(0\)	\(-12\)	\(0\)	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-12\zeta_{6}q^{5}+\cdots\)
882.4.g.q	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(0\)	\(-6\)	\(0\)	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots\)
882.4.g.r	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(0\)	\(-2\)	\(0\)	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
882.4.g.s	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(0\)	\(2\)	\(0\)	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
882.4.g.t	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(0\)	\(6\)	\(0\)	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\)
882.4.g.u	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(0\)	\(9\)	\(0\)	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+9\zeta_{6}q^{5}+\cdots\)
882.4.g.v	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(0\)	\(12\)	\(0\)	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+12\zeta_{6}q^{5}+\cdots\)
882.4.g.w	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(0\)	\(18\)	\(0\)	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+18\zeta_{6}q^{5}+\cdots\)
882.4.g.x	\(2\)	\(52.040\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(0\)	\(22\)	\(0\)	\(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+22\zeta_{6}q^{5}+\cdots\)
882.4.g.y	\(4\)	\(52.040\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	\(-4\)	\(0\)	\(-12\)	\(0\)	\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+(-6-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.z	\(4\)	\(52.040\)	\(\Q(\sqrt{-3}, \sqrt{193})\)	None	\(-4\)	\(0\)	\(-7\)	\(0\)	\(q-2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.ba	\(4\)	\(52.040\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	\(-4\)	\(0\)	\(0\)	\(0\)	\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+14\beta _{1}q^{5}+\cdots\)
882.4.g.bb	\(4\)	\(52.040\)	\(\Q(\sqrt{-3}, \sqrt{58})\)	None	\(-4\)	\(0\)	\(0\)	\(0\)	\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
882.4.g.bc	\(4\)	\(52.040\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	\(-4\)	\(0\)	\(0\)	\(0\)	\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+5\beta _{1}q^{5}+\cdots\)
882.4.g.bd	\(4\)	\(52.040\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	\(-4\)	\(0\)	\(12\)	\(0\)	\(q+(-2-2\beta _{2})q^{2}+4\beta _{2}q^{4}+(6+\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.be	\(4\)	\(52.040\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	\(4\)	\(0\)	\(-12\)	\(0\)	\(q-2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.bf	\(4\)	\(52.040\)	\(\Q(\sqrt{-3}, \sqrt{1345})\)	None	\(4\)	\(0\)	\(-5\)	\(0\)	\(q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.bg	\(4\)	\(52.040\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	\(4\)	\(0\)	\(0\)	\(0\)	\(q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+5\beta _{1}q^{5}+\cdots\)
882.4.g.bh	\(4\)	\(52.040\)	\(\Q(\sqrt{-3}, \sqrt{58})\)	None	\(4\)	\(0\)	\(0\)	\(0\)	\(q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots\)
882.4.g.bi	\(4\)	\(52.040\)	\(\Q(\sqrt{-3}, \sqrt{22})\)	None	\(4\)	\(0\)	\(0\)	\(0\)	\(q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots\)
882.4.g.bj	\(4\)	\(52.040\)	\(\Q(\sqrt{-3}, \sqrt{193})\)	None	\(4\)	\(0\)	\(7\)	\(0\)	\(q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
882.4.g.bk	\(4\)	\(52.040\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	\(4\)	\(0\)	\(12\)	\(0\)	\(q-2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

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Defining parameters

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

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

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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	$13$