Space of modular forms of level 38 and weight 6

• Label: 38.6
• Level: 38
• Weight: 6
• Dimension: 75
• Nonzero newspaces: 3
• Newform subspaces: 8
• Sturm bound: 540
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(540\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(38))\).

	Total	New	Old
Modular forms	243	75	168
Cusp forms	207	75	132
Eisenstein series	36	0	36

Trace form

75 * q + 864 * q^12 - 4344 * q^13 - 3960 * q^14 - 3564 * q^15 + 4302 * q^17 + 8748 * q^18 + 12810 * q^19 + 3168 * q^20 - 1890 * q^21 - 8532 * q^22 - 10278 * q^23 - 23364 * q^25 - 3960 * q^26 + 41157 * q^27 + 14304 * q^28 - 11358 * q^29 - 19638 * q^31 - 12906 * q^33 + 29556 * q^35 + 24642 * q^37 + 57726 * q^39 - 558 * q^41 - 2310 * q^43 + 32976 * q^44 - 118152 * q^45 - 60624 * q^46 - 177192 * q^47 - 25344 * q^48 - 65400 * q^49 - 115488 * q^50 + 45351 * q^51 + 2784 * q^52 + 105048 * q^53 + 123336 * q^54 + 205992 * q^55 + 112896 * q^56 + 277110 * q^57 + 96624 * q^58 + 177210 * q^59 + 35136 * q^60 + 21126 * q^61 - 84024 * q^62 - 268416 * q^63 - 24576 * q^64 - 545760 * q^65 - 391968 * q^66 - 372066 * q^67 - 36144 * q^68 - 89694 * q^69 + 77616 * q^70 + 452016 * q^71 + 138816 * q^72 + 274017 * q^73 + 236250 * q^75 + 498816 * q^77 + 421776 * q^78 + 241086 * q^79 - 452097 * q^81 - 286704 * q^82 - 553464 * q^83 - 439776 * q^84 - 494568 * q^85 - 180720 * q^86 - 739980 * q^87 - 6876 * q^89 + 363240 * q^90 + 519456 * q^91 + 265536 * q^92 + 1344798 * q^93 + 636192 * q^94 + 1251810 * q^95 + 387198 * q^97 + 371232 * q^98 - 197541 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(38))\)

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
38.6.a	\(\chi_{38}(1, \cdot)\)	38.6.a.a	1	1
		38.6.a.b	1
		38.6.a.c	2
		38.6.a.d	3
38.6.c	\(\chi_{38}(7, \cdot)\)	38.6.c.a	6	2
		38.6.c.b	8
38.6.e	\(\chi_{38}(5, \cdot)\)	38.6.e.a	24	6
		38.6.e.b	30

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(38))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(38)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 1}\)