Space of modular forms of level 176, weight 10, and trivial character

• Label: 176.10.a
• Level: $176$
• Weight: $10$
• Character orbit: 176.a
• Rep. character: $\chi_{176}(1,\cdot)$
• Character field: $\Q$
• Dimension: $45$
• Newform subspaces: $13$
• Sturm bound: $240$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	176.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(240\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(176))\).

	Total	New	Old
Modular forms	222	45	177
Cusp forms	210	45	165
Eisenstein series	12	0	12

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

\(2\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(10\)
\(+\)	\(-\)	$-$	\(13\)
\(-\)	\(+\)	$-$	\(11\)
\(-\)	\(-\)	$+$	\(11\)
Plus space		\(+\)	\(21\)
Minus space		\(-\)	\(24\)

Trace form

\( 45 q + 162 q^{3} + 718 q^{5} + 2052 q^{7} + 295245 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(176))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	11
176.10.a.a	$176$	$10$	176.a	1.a	$1$	$1$	$1$	$90.646$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-201\)	\(2349\)	\(8806\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-201q^{3}+2349q^{5}+8806q^{7}+20718q^{9}+\cdots\)
176.10.a.b	$176$	$10$	176.a	1.a	$1$	$1$	$1$	$90.646$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-137\)	\(-595\)	\(-11354\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-137q^{3}-595q^{5}-11354q^{7}-914q^{9}+\cdots\)
176.10.a.c	$176$	$10$	176.a	1.a	$1$	$1$	$1$	$90.646$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(41\)	\(-1039\)	\(3482\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+41q^{3}-1039q^{5}+3482q^{7}-18002q^{9}+\cdots\)
176.10.a.d	$176$	$10$	176.a	1.a	$1$	$2$	$2$	$90.646$	\(\Q(\sqrt{463}) \)	None	✓	$1$	$1$	\(0\)	\(-34\)	\(-1478\)	\(-8196\)		$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-17+\beta )q^{3}+(-739+10\beta )q^{5}+\cdots\)
176.10.a.e	$176$	$10$	176.a	1.a	$1$	$2$	$2$	$90.646$	\(\Q(\sqrt{889}) \)	None	✓	$1$	$0$	\(0\)	\(21\)	\(-521\)	\(7490\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(6+9\beta )q^{3}+(-212-97\beta )q^{5}+(3580+\cdots)q^{7}+\cdots\)
176.10.a.f	$176$	$10$	176.a	1.a	$1$	$3$	$3$	$90.646$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(131\)	\(1011\)	\(2230\)		$-$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(44-\beta _{1})q^{3}+(337+\beta _{1}-\beta _{2})q^{5}+\cdots\)
176.10.a.g	$176$	$10$	176.a	1.a	$1$	$3$	$3$	$90.646$	3.3.2659452.1	None	✓	$1$	$1$	\(0\)	\(186\)	\(-1824\)	\(7260\)		$-$	$-$	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+(62-2\beta _{1}+\beta _{2})q^{3}+(-608+17\beta _{1}+\cdots)q^{5}+\cdots\)
176.10.a.h	$176$	$10$	176.a	1.a	$1$	$4$	$4$	$90.646$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(105\)	\(93\)	\(-1318\)		$-$	$-$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(26+\beta _{1})q^{3}+(5^{2}-5\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
176.10.a.i	$176$	$10$	176.a	1.a	$1$	$5$	$5$	$90.646$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-152\)	\(1898\)	\(-13496\)		$+$	$+$	$+$	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-30-\beta _{1})q^{3}+(380-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
176.10.a.j	$176$	$10$	176.a	1.a	$1$	$5$	$5$	$90.646$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-112\)	\(1594\)	\(-8400\)		$-$	$+$	$-$	$2^{12}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-22+\beta _{2})q^{3}+(320-2\beta _{1}+4\beta _{2}+\cdots)q^{5}+\cdots\)
176.10.a.k	$176$	$10$	176.a	1.a	$1$	$5$	$5$	$90.646$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(152\)	\(-1334\)	\(9720\)		$+$	$+$	$+$	$2^{10}\cdot 3$	$\mathrm{SU}(2)$	\(q+(30+\beta _{1})q^{3}+(-266-2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
176.10.a.l	$176$	$10$	176.a	1.a	$1$	$6$	$6$	$90.646$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(91\)	\(23\)	\(5738\)		$+$	$-$	$-$	$2^{19}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(15+\beta _{2})q^{3}+(4+\beta _{1})q^{5}+(957+\beta _{1}+\cdots)q^{7}+\cdots\)
176.10.a.m	$176$	$10$	176.a	1.a	$1$	$7$	$7$	$90.646$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(71\)	\(541\)	\(90\)		$+$	$-$	$-$	$2^{26}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(10-\beta _{1})q^{3}+(77-2\beta _{1}+\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(176))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(176)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 2}\)