Space of modular forms of level 625, weight 2, and Character 625.d

• Label: 625.2.d
• Level: $625$
• Weight: $2$
• Character orbit: 625.d
• Rep. character: $\chi_{625}(126,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $136$
• Newform subspaces: $17$
• Sturm bound: $125$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.d (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(125\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(625, [\chi])\).

	Total	New	Old
Modular forms	308	184	124
Cusp forms	188	136	52
Eisenstein series	120	48	72

Trace form

136 * q - 28 * q^4 + 12 * q^6 - 22 * q^9 + 12 * q^11 + 24 * q^14 - 4 * q^16 + 12 * q^21 - 40 * q^24 - 68 * q^26 - 20 * q^29 + 12 * q^31 + 14 * q^34 - 24 * q^36 - 24 * q^39 - 8 * q^41 - 16 * q^44 + 12 * q^46 - 8 * q^49 - 48 * q^51 + 60 * q^54 - 20 * q^56 - 8 * q^61 + 32 * q^64 - 36 * q^66 + 36 * q^69 - 28 * q^71 - 36 * q^74 - 80 * q^76 - 14 * q^81 + 104 * q^84 + 12 * q^86 - 10 * q^89 + 12 * q^91 - 106 * q^94 - 78 * q^96 - 64 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(625, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
625.2.d.a	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	\(\Q(\zeta_{10})\)	None					125.2.a.a	$2$	$0$	\(-3\)	\(-4\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}^{3})q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)
625.2.d.b	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	\(\Q(\zeta_{10})\)	None					25.2.d.a	$2$	$0$	\(-3\)	\(1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
625.2.d.c	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	\(\Q(\zeta_{10})\)	None		✓			625.2.a.a	$2$	$0$	\(-3\)	\(1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}^{3})q^{2}+(1-\zeta_{10}-2\zeta_{10}^{3})q^{3}+\cdots\)
625.2.d.d	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	\(\Q(\zeta_{10})\)	None					125.2.a.a	$2$	$1$	\(-2\)	\(-1\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}+\cdots)q^{3}+\cdots\)
625.2.d.e	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	\(\Q(\zeta_{10})\)	None		✓			625.2.a.a	$2$	$0$	\(-2\)	\(4\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{3})q^{3}+\cdots\)
625.2.d.f	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	\(\Q(\zeta_{10})\)	None		✓			625.2.a.a	$2$	$0$	\(2\)	\(-4\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)
625.2.d.g	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	\(\Q(\zeta_{10})\)	None					125.2.a.a	$2$	$0$	\(2\)	\(1\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}-2\zeta_{10}^{3})q^{3}+\cdots\)
625.2.d.h	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	\(\Q(\zeta_{10})\)	None					25.2.d.a	$2$	$0$	\(3\)	\(-1\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
625.2.d.i	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	\(\Q(\zeta_{10})\)	None		✓			625.2.a.a	$2$	$0$	\(3\)	\(-1\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}^{3})q^{2}+(-1+\zeta_{10}+2\zeta_{10}^{3})q^{3}+\cdots\)
625.2.d.j	$625$	$2$	625.d	25.d	$5$	$4$	$1$	$4.991$	\(\Q(\zeta_{10})\)	None					125.2.a.a	$2$	$0$	\(3\)	\(4\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}^{3})q^{2}+(1-\zeta_{10}+\zeta_{10}^{3})q^{3}+\cdots\)
625.2.d.k	$625$	$2$	625.d	25.d	$5$	$8$	$2$	$4.991$	8.0.484000000.9	None					125.2.a.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{1}-\beta _{6})q^{2}+(-\beta _{1}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
625.2.d.l	$625$	$2$	625.d	25.d	$5$	$8$	$2$	$4.991$	8.0.484000000.9	None					125.2.a.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{1}-\beta _{4})q^{2}-\beta _{1}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
625.2.d.m	$625$	$2$	625.d	25.d	$5$	$16$	$4$	$4.991$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			625.2.a.e	$2$	$0$	\(-5\)	\(0\)	\(0\)	\(20\)	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{1}+\beta _{3}+\beta _{4}-\beta _{6})q^{2}+(\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
625.2.d.n	$625$	$2$	625.d	25.d	$5$	$16$	$4$	$4.991$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			625.2.a.e	$2$	$0$	\(0\)	\(-5\)	\(0\)	\(20\)	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{5}-\beta _{6}+\beta _{7}-\beta _{8}-\beta _{12})q^{2}+\cdots\)
625.2.d.o	$625$	$2$	625.d	25.d	$5$	$16$	$4$	$4.991$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					25.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{1}-\beta _{11}-\beta _{13})q^{2}+(-\beta _{6}+\beta _{11}+\cdots)q^{3}+\cdots\)
625.2.d.p	$625$	$2$	625.d	25.d	$5$	$16$	$4$	$4.991$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			625.2.a.e	$2$	$0$	\(0\)	\(5\)	\(0\)	\(-20\)	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{5}+\beta _{6}-\beta _{7}+\beta _{8}+\beta _{12})q^{2}+(1+\cdots)q^{3}+\cdots\)
625.2.d.q	$625$	$2$	625.d	25.d	$5$	$16$	$4$	$4.991$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			625.2.a.e	$2$	$0$	\(5\)	\(0\)	\(0\)	\(-20\)	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1+\beta _{3}-\beta _{5}-\beta _{7})q^{2}+(\beta _{5}-\beta _{15})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(625, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(625, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 2}\)