Space of modular forms of level 175, weight 10, and Character 175.b

• Label: 175.10.b
• Level: $175$
• Weight: $10$
• Character orbit: 175.b
• Rep. character: $\chi_{175}(99,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $9$
• Sturm bound: $200$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	175.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(200\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(175, [\chi])\).

	Total	New	Old
Modular forms	186	82	104
Cusp forms	174	82	92
Eisenstein series	12	0	12

Trace form

82 * q - 22872 * q^4 - 12312 * q^6 - 522294 * q^9 + 147952 * q^11 - 153664 * q^14 + 8850568 * q^16 - 1861344 * q^19 + 739508 * q^21 + 8296876 * q^24 + 16305324 * q^26 - 1301356 * q^29 - 18049896 * q^31 + 34344344 * q^34 + 75013092 * q^36 - 59831696 * q^39 + 46753160 * q^41 + 131466630 * q^44 - 120337654 * q^46 - 472713682 * q^49 + 146040476 * q^51 + 724921252 * q^54 + 96246486 * q^56 + 356269412 * q^59 + 143787416 * q^61 - 2222716926 * q^64 - 1426012396 * q^66 - 1808650968 * q^69 + 611907964 * q^71 + 831359154 * q^74 - 1433005284 * q^76 - 1303654700 * q^79 + 3447882298 * q^81 - 558107648 * q^84 + 1054172358 * q^86 + 1482306264 * q^89 + 1407946400 * q^91 + 819507428 * q^94 - 2829797556 * q^96 - 6788024404 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(175, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
175.10.b.a	$175$	$10$	175.b	5.b	$2$	$2$	$2$	$90.131$	\(\Q(\sqrt{-1}) \)	None					35.10.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+28 i q^{2}+116 i q^{3}-272 q^{4}+\cdots\)
175.10.b.b	$175$	$10$	175.b	5.b	$2$	$4$	$4$	$90.131$	\(\Q(i, \sqrt{193})\)	None					7.10.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3\beta _{1}+\beta _{2})q^{2}+(43\beta _{1}+11\beta _{2}+\cdots)q^{3}+\cdots\)
175.10.b.c	$175$	$10$	175.b	5.b	$2$	$4$	$4$	$90.131$	\(\Q(\zeta_{8})\)	None					35.10.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+12\beta_1)q^{2}+(54\beta_{2}-87\beta_1)q^{3}+\cdots\)
175.10.b.d	$175$	$10$	175.b	5.b	$2$	$6$	$6$	$90.131$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None					7.10.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-7\beta _{1}-\beta _{4})q^{2}+(28\beta _{1}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
175.10.b.e	$175$	$10$	175.b	5.b	$2$	$8$	$8$	$90.131$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					35.10.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(5\beta _{4}-\beta _{5})q^{2}+(-4\beta _{4}+\beta _{6})q^{3}+\cdots\)
175.10.b.f	$175$	$10$	175.b	5.b	$2$	$10$	$10$	$90.131$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					35.10.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(-28\beta _{1}+\beta _{2})q^{3}+(-168+\cdots)q^{4}+\cdots\)
175.10.b.g	$175$	$10$	175.b	5.b	$2$	$12$	$12$	$90.131$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					35.10.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+2\beta _{7})q^{2}+(-\beta _{1}+21\beta _{7}+\beta _{8}+\cdots)q^{3}+\cdots\)
175.10.b.h	$175$	$10$	175.b	5.b	$2$	$16$	$16$	$90.131$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			175.10.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{15}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-3\beta _{9})q^{2}+(\beta _{1}-8\beta _{9}+\beta _{10}+\cdots)q^{3}+\cdots\)
175.10.b.i	$175$	$10$	175.b	5.b	$2$	$20$	$20$	$90.131$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓		175.10.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{15}\cdot 3^{8}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\beta _{10}+\beta _{11})q^{2}+(8\beta _{10}-\beta _{13})q^{3}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(175, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)