Space of modular forms of level 156 and weight 2

• Label: 156.2
• Level: 156
• Weight: 2
• Dimension: 270
• Nonzero newspaces: 12
• Newform subspaces: 32
• Sturm bound: 2688
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 32 \)
Sturm bound:			\(2688\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(156))\).

	Total	New	Old
Modular forms	792	310	482
Cusp forms	553	270	283
Eisenstein series	239	40	199

Trace form

270 * q - 12 * q^4 - 6 * q^6 + 4 * q^7 - 10 * q^9 - 12 * q^10 + 12 * q^11 - 12 * q^12 + 12 * q^15 - 12 * q^16 + 6 * q^17 - 24 * q^18 - 8 * q^19 - 48 * q^20 - 34 * q^21 - 72 * q^22 - 24 * q^23 - 54 * q^24 - 78 * q^25 - 60 * q^26 - 36 * q^27 - 72 * q^28 - 30 * q^29 - 54 * q^30 - 24 * q^31 - 60 * q^32 - 54 * q^33 - 60 * q^34 - 24 * q^35 - 24 * q^36 - 30 * q^37 - 28 * q^39 + 24 * q^40 - 66 * q^41 + 12 * q^42 - 32 * q^43 + 60 * q^44 - 60 * q^45 + 108 * q^46 - 24 * q^47 + 42 * q^48 - 176 * q^49 + 108 * q^50 - 24 * q^51 + 96 * q^52 - 48 * q^53 - 18 * q^54 - 12 * q^55 + 108 * q^56 - 58 * q^57 + 84 * q^58 + 12 * q^59 + 84 * q^60 - 90 * q^61 + 60 * q^62 + 62 * q^63 + 48 * q^64 - 18 * q^65 + 72 * q^66 + 40 * q^67 + 66 * q^69 + 48 * q^70 + 24 * q^71 + 72 * q^72 + 16 * q^73 + 104 * q^75 - 12 * q^76 + 72 * q^77 + 108 * q^78 + 72 * q^79 + 50 * q^81 - 12 * q^82 + 36 * q^83 + 120 * q^84 + 54 * q^85 + 48 * q^86 + 84 * q^87 + 48 * q^88 + 72 * q^89 + 144 * q^90 + 52 * q^91 + 72 * q^92 + 74 * q^93 + 84 * q^94 + 48 * q^95 + 120 * q^96 + 60 * q^97 + 108 * q^98 - 18 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)

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
156.2.a	\(\chi_{156}(1, \cdot)\)	156.2.a.a	1	1
		156.2.a.b	1
156.2.b	\(\chi_{156}(25, \cdot)\)	156.2.b.a	2	1
		156.2.b.b	2
156.2.c	\(\chi_{156}(131, \cdot)\)	156.2.c.a	2	1
		156.2.c.b	2
		156.2.c.c	8
		156.2.c.d	12
156.2.h	\(\chi_{156}(155, \cdot)\)	156.2.h.a	8	1
		156.2.h.b	16
156.2.i	\(\chi_{156}(61, \cdot)\)	156.2.i.a	2	2
156.2.k	\(\chi_{156}(31, \cdot)\)	156.2.k.a	2	2
		156.2.k.b	2
		156.2.k.c	2
		156.2.k.d	2
		156.2.k.e	10
		156.2.k.f	10
156.2.m	\(\chi_{156}(5, \cdot)\)	156.2.m.a	4	2
		156.2.m.b	4
156.2.p	\(\chi_{156}(35, \cdot)\)	156.2.p.a	8	2
		156.2.p.b	40
156.2.q	\(\chi_{156}(49, \cdot)\)	156.2.q.a	2	2
		156.2.q.b	4
156.2.r	\(\chi_{156}(23, \cdot)\)	156.2.r.a	4	2
		156.2.r.b	4
		156.2.r.c	40
156.2.u	\(\chi_{156}(41, \cdot)\)	156.2.u.a	4	4
		156.2.u.b	16
156.2.w	\(\chi_{156}(7, \cdot)\)	156.2.w.a	4	4
		156.2.w.b	4
		156.2.w.c	24
		156.2.w.d	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(156))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(156)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)