Space of modular forms of level 7 and weight 7

• Label: 7.7
• Level: 7
• Weight: 7
• Dimension: 9
• Nonzero newspaces: 2
• Newform subspaces: 4
• Sturm bound: 28
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 7 \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(28\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(7))\).

	Total	New	Old
Modular forms	15	15	0
Cusp forms	9	9	0
Eisenstein series	6	6	0

Trace form

9 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 165 * q^5 - 483 * q^7 - 711 * q^8 - 1851 * q^9 + 2580 * q^10 + 4113 * q^11 + 5964 * q^12 - 11151 * q^14 - 16830 * q^15 - 10023 * q^16 + 8229 * q^17 + 34209 * q^18 + 29985 * q^19 - 37527 * q^21 - 59910 * q^22 - 4875 * q^23 + 28872 * q^24 + 62745 * q^25 + 33768 * q^26 - 23835 * q^28 - 25518 * q^29 - 43200 * q^30 - 39399 * q^31 - 56055 * q^32 - 36711 * q^33 + 74865 * q^35 + 187881 * q^36 + 124905 * q^37 + 60960 * q^38 - 183372 * q^39 - 137280 * q^40 + 206136 * q^42 + 221610 * q^43 - 89298 * q^44 - 370530 * q^45 - 465006 * q^46 - 407823 * q^47 + 328545 * q^49 + 502065 * q^50 + 603369 * q^51 + 128856 * q^52 + 62577 * q^53 - 44496 * q^54 + 66801 * q^56 - 423054 * q^57 - 381030 * q^58 - 436299 * q^59 - 207900 * q^60 + 141201 * q^61 - 217875 * q^63 - 93999 * q^64 + 210420 * q^65 + 1025532 * q^66 + 1637829 * q^67 + 799596 * q^68 - 1863120 * q^70 - 1888974 * q^71 - 1509759 * q^72 - 421599 * q^73 + 173814 * q^74 + 826050 * q^75 + 709485 * q^77 + 330624 * q^78 + 433269 * q^79 + 2654040 * q^80 + 1867068 * q^81 + 2585016 * q^82 - 1982148 * q^84 - 2215950 * q^85 - 2589894 * q^86 - 1909746 * q^87 - 491598 * q^88 - 2990823 * q^89 - 687960 * q^91 + 791898 * q^92 + 3031977 * q^93 + 223584 * q^94 + 1240005 * q^95 + 972720 * q^96 + 3425541 * q^98 + 1018098 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(7))\)

We only show spaces with odd 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
7.7.b	\(\chi_{7}(6, \cdot)\)	7.7.b.a	1	1
		7.7.b.b	2
7.7.d	\(\chi_{7}(3, \cdot)\)	7.7.d.a	2	2
		7.7.d.b	4