Space of modular forms of level 2, weight 10, and trivial character

• Label: 2.10.a
• Level: $2$
• Weight: $10$
• Character orbit: 2.a
• Rep. character: $\chi_{2}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $2$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(2\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(2))\).

	Total	New	Old
Modular forms	3	1	2
Cusp forms	1	1	0
Eisenstein series	2	0	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	Dim
\(-\)	\(1\)

Trace form

q + 16 * q^2 - 156 * q^3 + 256 * q^4 + 870 * q^5 - 2496 * q^6 - 952 * q^7 + 4096 * q^8 + 4653 * q^9 + 13920 * q^10 - 56148 * q^11 - 39936 * q^12 + 178094 * q^13 - 15232 * q^14 - 135720 * q^15 + 65536 * q^16 - 247662 * q^17 + 74448 * q^18 + 315380 * q^19 + 222720 * q^20 + 148512 * q^21 - 898368 * q^22 + 204504 * q^23 - 638976 * q^24 - 1196225 * q^25 + 2849504 * q^26 + 2344680 * q^27 - 243712 * q^28 - 3840450 * q^29 - 2171520 * q^30 - 1309408 * q^31 + 1048576 * q^32 + 8759088 * q^33 - 3962592 * q^34 - 828240 * q^35 + 1191168 * q^36 + 4307078 * q^37 + 5046080 * q^38 - 27782664 * q^39 + 3563520 * q^40 + 1512042 * q^41 + 2376192 * q^42 + 33670604 * q^43 - 14373888 * q^44 + 4048110 * q^45 + 3272064 * q^46 - 10581072 * q^47 - 10223616 * q^48 - 39447303 * q^49 - 19139600 * q^50 + 38635272 * q^51 + 45592064 * q^52 + 16616214 * q^53 + 37514880 * q^54 - 48848760 * q^55 - 3899392 * q^56 - 49199280 * q^57 - 61447200 * q^58 + 112235100 * q^59 - 34744320 * q^60 - 33197218 * q^61 - 20950528 * q^62 - 4429656 * q^63 + 16777216 * q^64 + 154941780 * q^65 + 140145408 * q^66 - 121372252 * q^67 - 63401472 * q^68 - 31902624 * q^69 - 13251840 * q^70 - 387172728 * q^71 + 19058688 * q^72 + 255240074 * q^73 + 68913248 * q^74 + 186611100 * q^75 + 80737280 * q^76 + 53452896 * q^77 - 444522624 * q^78 + 492101840 * q^79 + 57016320 * q^80 - 457355079 * q^81 + 24192672 * q^82 - 457420236 * q^83 + 38019072 * q^84 - 215465940 * q^85 + 538729664 * q^86 + 599110200 * q^87 - 229982208 * q^88 - 31809510 * q^89 + 64769760 * q^90 - 169545488 * q^91 + 52353024 * q^92 + 204267648 * q^93 - 169297152 * q^94 + 274380600 * q^95 - 163577856 * q^96 - 673532062 * q^97 - 631156848 * q^98 - 261256644 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2
2.10.a.a	$2$	$10$	2.a	1.a	$1$	$1$	$1$	$1.030$	\(\Q\)	None	✓	✓	✓	✓	2.10.a.a	$1$	$0$	\(16\)	\(-156\)	\(870\)	\(-952\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}-156q^{3}+2^{8}q^{4}+870q^{5}+\cdots\)