Space of modular forms of level 7 and weight 4

• Label: 7.4
• Level: 7
• Weight: 4
• Dimension: 3
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 16
• Trace bound: 1

Defining parameters

Level:	$N$	=	$7$
Weight:	$k$	=	$4$
Nonzero newspaces:			$2$
Newform subspaces:			$2$
Sturm bound:			$16$
Trace bound:			$1$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(\Gamma_1(7))$.

	Total	New	Old
Modular forms	9	7	2
Cusp forms	3	3	0
Eisenstein series	6	4	2

Trace form

3 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 + 9 * q^5 + 30 * q^6 + 21 * q^7 - 33 * q^8 - 45 * q^9 - 30 * q^10 - 3 * q^11 + 42 * q^12 + 21 * q^14 + 66 * q^15 + 57 * q^16 + 75 * q^17 - 21 * q^18 - 159 * q^19 - 168 * q^20 - 231 * q^21 - 12 * q^22 + 207 * q^23 + 138 * q^24 + 207 * q^25 + 30 * q^27 + 189 * q^28 + 6 * q^29 - 66 * q^30 - 135 * q^31 - 321 * q^32 + 51 * q^33 - 138 * q^34 - 63 * q^35 - 15 * q^36 - 465 * q^37 + 12 * q^38 + 42 * q^39 + 408 * q^40 + 882 * q^41 + 378 * q^42 - 120 * q^43 + 36 * q^44 - 522 * q^45 + 270 * q^46 - 201 * q^47 - 306 * q^48 + 147 * q^49 - 435 * q^50 + 39 * q^51 - 252 * q^52 - 465 * q^53 - 30 * q^54 - 198 * q^55 - 777 * q^56 + 906 * q^57 - 6 * q^58 + 915 * q^59 + 420 * q^60 - 75 * q^61 + 576 * q^62 + 315 * q^63 + 729 * q^64 + 546 * q^65 + 54 * q^66 - 171 * q^67 - 462 * q^68 - 2322 * q^69 - 378 * q^70 - 1632 * q^71 + 183 * q^72 + 411 * q^73 - 192 * q^74 + 270 * q^75 + 378 * q^76 + 231 * q^77 - 336 * q^78 + 543 * q^79 + 768 * q^80 + 1260 * q^81 - 882 * q^82 + 882 * q^83 - 294 * q^84 + 570 * q^85 + 120 * q^86 - 186 * q^87 - 240 * q^88 + 1059 * q^89 + 984 * q^90 - 588 * q^91 + 936 * q^92 - 1053 * q^93 - 1374 * q^94 - 2103 * q^95 - 798 * q^96 - 1470 * q^97 + 1029 * q^98 - 36 * q^99

Decomposition of $S_{4}^{\mathrm{new}}(\Gamma_1(7))$

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
7.4.a	$\chi_{7}(1, \cdot)$	7.4.a.a	1	1
7.4.c	$\chi_{7}(2, \cdot)$	7.4.c.a	2	2