Space of modular forms of level 44 and weight 2

• Label: 44.2
• Level: 44
• Weight: 2
• Dimension: 25
• Nonzero newspaces: 4
• Newform subspaces: 4
• Sturm bound: 240
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(240\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(44))\).

	Total	New	Old
Modular forms	85	45	40
Cusp forms	36	25	11
Eisenstein series	49	20	29

Trace form

25 * q - 5 * q^2 - 5 * q^4 - 10 * q^5 - 5 * q^6 - 5 * q^7 - 5 * q^8 - 20 * q^9 - 5 * q^11 - 10 * q^12 - 15 * q^13 + 15 * q^16 - 5 * q^17 + 20 * q^18 + 15 * q^19 + 20 * q^20 + 20 * q^21 + 25 * q^22 + 5 * q^23 + 25 * q^24 + 20 * q^26 + 20 * q^28 - 15 * q^29 - 20 * q^33 - 30 * q^34 - 15 * q^35 - 30 * q^36 + 20 * q^37 - 30 * q^38 + 5 * q^39 - 40 * q^40 + 5 * q^41 - 50 * q^42 - 10 * q^43 - 40 * q^44 + 30 * q^45 - 30 * q^46 - 5 * q^47 - 60 * q^48 - 5 * q^49 - 15 * q^50 + 5 * q^51 - 10 * q^52 + 35 * q^53 + 10 * q^55 + 20 * q^56 + 25 * q^57 + 30 * q^58 + 20 * q^59 + 40 * q^60 - 15 * q^61 + 70 * q^62 + 55 * q^64 + 10 * q^65 + 60 * q^66 + 15 * q^67 + 60 * q^68 + 25 * q^69 + 20 * q^70 + 20 * q^71 + 45 * q^72 - 15 * q^73 + 40 * q^74 - 5 * q^75 + 5 * q^77 - 20 * q^78 + 5 * q^79 - 20 * q^80 - 55 * q^81 - 35 * q^82 - 25 * q^83 - 10 * q^84 - 75 * q^85 - 55 * q^86 - 50 * q^87 - 85 * q^88 - 65 * q^89 - 50 * q^90 - 35 * q^91 - 40 * q^93 - 30 * q^94 - 25 * q^95 - 20 * q^97 + 10 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)

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
44.2.a	\(\chi_{44}(1, \cdot)\)	44.2.a.a	1	1
44.2.c	\(\chi_{44}(43, \cdot)\)	44.2.c.a	4	1
44.2.e	\(\chi_{44}(5, \cdot)\)	44.2.e.a	4	4
44.2.g	\(\chi_{44}(7, \cdot)\)	44.2.g.a	16	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(44))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(44)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)