Space of modular forms of level 3174 and weight 2

• Label: 3174.2
• Level: 3174
• Weight: 2
• Dimension: 69563
• Nonzero newspaces: 8
• Sturm bound: 1117248
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 3174 = 2 \cdot 3 \cdot 23^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(1117248\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3174))\).

	Total	New	Old
Modular forms	282304	69563	212741
Cusp forms	276321	69563	206758
Eisenstein series	5983	0	5983

Trace form

69563 * q - q^2 - q^3 - q^4 - 6 * q^5 - q^6 - 8 * q^7 - q^8 - q^9 - 6 * q^10 - 12 * q^11 - q^12 - 14 * q^13 - 8 * q^14 + 38 * q^15 - q^16 + 70 * q^17 + 87 * q^18 + 68 * q^19 + 82 * q^20 + 124 * q^21 + 76 * q^22 + 88 * q^23 - q^24 + 145 * q^25 + 74 * q^26 + 131 * q^27 + 80 * q^28 + 58 * q^29 + 82 * q^30 + 56 * q^31 - q^32 + 32 * q^33 - 18 * q^34 + 40 * q^35 - q^36 + 138 * q^37 - 20 * q^38 + 74 * q^39 - 6 * q^40 + 46 * q^41 - 8 * q^42 + 132 * q^43 - 12 * q^44 - 6 * q^45 + 128 * q^47 - q^48 + 207 * q^49 - 31 * q^50 + 70 * q^51 - 14 * q^52 + 34 * q^53 - 45 * q^54 + 104 * q^55 - 8 * q^56 - 64 * q^57 - 30 * q^58 + 28 * q^59 - 50 * q^60 - 62 * q^61 - 32 * q^62 - 228 * q^63 - q^64 - 84 * q^65 - 188 * q^66 - 68 * q^67 - 18 * q^68 - 110 * q^69 - 48 * q^70 - 72 * q^71 - 89 * q^72 - 74 * q^73 - 38 * q^74 - 295 * q^75 - 20 * q^76 - 96 * q^77 - 146 * q^78 + 8 * q^79 - 6 * q^80 - 89 * q^81 - 42 * q^82 + 4 * q^83 - 52 * q^84 - 20 * q^85 - 44 * q^86 + 102 * q^87 - 12 * q^88 - 2 * q^89 - 6 * q^90 + 64 * q^91 - 32 * q^93 - 48 * q^94 + 144 * q^95 - q^96 + 254 * q^97 + 119 * q^98 + 208 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3174))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
3174.2.a	\(\chi_{3174}(1, \cdot)\)	3174.2.a.a	1	1
		3174.2.a.b	1
		3174.2.a.c	1
		3174.2.a.d	1
		3174.2.a.e	1
		3174.2.a.f	1
		3174.2.a.g	1
		3174.2.a.h	2
		3174.2.a.i	2
		3174.2.a.j	2
		3174.2.a.k	2
		3174.2.a.l	2
		3174.2.a.m	2
		3174.2.a.n	2
		3174.2.a.o	2
		3174.2.a.p	2
		3174.2.a.q	2
		3174.2.a.r	2
		3174.2.a.s	2
		3174.2.a.t	4
		3174.2.a.u	4
		3174.2.a.v	4
		3174.2.a.w	5
		3174.2.a.x	5
		3174.2.a.y	5
		3174.2.a.z	5
		3174.2.a.ba	5
		3174.2.a.bb	5
		3174.2.a.bc	5
		3174.2.a.bd	5
3174.2.d	\(\chi_{3174}(3173, \cdot)\)	n/a	168	1
3174.2.e	\(\chi_{3174}(487, \cdot)\)	n/a	840	10
3174.2.f	\(\chi_{3174}(263, \cdot)\)	n/a	1680	10
3174.2.i	\(\chi_{3174}(139, \cdot)\)	n/a	2024	22
3174.2.j	\(\chi_{3174}(137, \cdot)\)	n/a	4048	22
3174.2.m	\(\chi_{3174}(13, \cdot)\)	n/a	20240	220
3174.2.p	\(\chi_{3174}(5, \cdot)\)	n/a	40480	220

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3174))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3174)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1058))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1587))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3174))\)\(^{\oplus 1}\)