Space of modular forms of level 1532 and weight 2

• Label: 1532.2
• Level: 1532
• Weight: 2
• Dimension: 42402
• Nonzero newspaces: 4
• Sturm bound: 293376
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1532 = 2^{2} \cdot 383 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(293376\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1532))\).

	Total	New	Old
Modular forms	74299	43166	31133
Cusp forms	72390	42402	29988
Eisenstein series	1909	764	1145

Trace form

42402 * q - 191 * q^2 - 191 * q^4 - 382 * q^5 - 191 * q^6 - 191 * q^8 - 382 * q^9 - 191 * q^10 - 191 * q^12 - 382 * q^13 - 191 * q^14 - 191 * q^16 - 382 * q^17 - 191 * q^18 - 191 * q^20 - 382 * q^21 - 191 * q^22 - 191 * q^24 - 382 * q^25 - 191 * q^26 - 191 * q^28 - 382 * q^29 - 191 * q^30 - 191 * q^32 - 382 * q^33 - 191 * q^34 - 191 * q^36 - 382 * q^37 - 191 * q^38 - 191 * q^40 - 382 * q^41 - 191 * q^42 - 191 * q^44 - 382 * q^45 - 191 * q^46 - 191 * q^48 - 382 * q^49 - 191 * q^50 - 191 * q^52 - 382 * q^53 - 191 * q^54 - 191 * q^56 - 382 * q^57 - 191 * q^58 - 191 * q^60 - 382 * q^61 - 191 * q^62 - 191 * q^64 - 382 * q^65 - 191 * q^66 - 191 * q^68 - 382 * q^69 - 191 * q^70 - 191 * q^72 - 382 * q^73 - 191 * q^74 - 191 * q^76 - 382 * q^77 - 191 * q^78 - 191 * q^80 - 382 * q^81 - 191 * q^82 - 191 * q^84 - 382 * q^85 - 191 * q^86 - 191 * q^88 - 382 * q^89 - 191 * q^90 - 191 * q^92 - 382 * q^93 - 191 * q^94 - 191 * q^96 - 382 * q^97 - 191 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1532))\)

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
1532.2.a	\(\chi_{1532}(1, \cdot)\)	1532.2.a.a	4	1
		1532.2.a.b	12
		1532.2.a.c	16
1532.2.b	\(\chi_{1532}(1531, \cdot)\)	n/a	190	1
1532.2.e	\(\chi_{1532}(9, \cdot)\)	n/a	6080	190
1532.2.h	\(\chi_{1532}(11, \cdot)\)	n/a	36100	190

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1532))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1532)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(383))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(766))\)\(^{\oplus 2}\)