↑

Properties

Label 7.26.a
Level $7$
Weight $26$
Character orbit 7.a
Rep. character $\chi_{7}(1,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $2$
Sturm bound $17$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 7.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(17\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(7))\).

Total New Old
Modular forms 17 13 4
Cusp forms 15 13 2
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(7\)Dim
\(+\)\(6\)
\(-\)\(7\)

Trace form

\( 13 q + 4143 q^{2} - 671276 q^{3} + 286290985 q^{4} + 595482126 q^{5} - 16200322 q^{6} + 13841287201 q^{7} + 298019175135 q^{8} + 3766873461193 q^{9} + O(q^{10}) \) \( 13 q + 4143 q^{2} - 671276 q^{3} + 286290985 q^{4} + 595482126 q^{5} - 16200322 q^{6} + 13841287201 q^{7} + 298019175135 q^{8} + 3766873461193 q^{9} - 7909038913836 q^{10} - 9521138710500 q^{11} + 11612746483478 q^{12} - 70582774898986 q^{13} + 174441742594203 q^{14} + 689833422068728 q^{15} + 3842800094397601 q^{16} + 1629554562435978 q^{17} + 5925847823995319 q^{18} + 14304619419287492 q^{19} - 43227116529364488 q^{20} - 7295299562456668 q^{21} - 29619885928398504 q^{22} + 258975579242845464 q^{23} - 293278061401892718 q^{24} + 84095131709707123 q^{25} + 581013759377982336 q^{26} - 4247067566187004760 q^{27} + 1563710244759560737 q^{28} + 3751799681210138598 q^{29} + 8360278000216451792 q^{30} + 2899460509988418176 q^{31} + 6127143123638334303 q^{32} - 10149222462175517552 q^{33} + 57499253264374483746 q^{34} + 5192689859714645862 q^{35} - 12651749629790903047 q^{36} - 89140241162505018802 q^{37} - 34573726926349323150 q^{38} + 58386736019878405720 q^{39} + 16164931018798945776 q^{40} + 258383390625140595234 q^{41} + 15415381802275674982 q^{42} + 67361272082297643644 q^{43} - 343394546722854206352 q^{44} - 2449959328535744127530 q^{45} + 1736743995271119886512 q^{46} + 747673593094717066128 q^{47} + 512458361678815450334 q^{48} + 2490556007947363387213 q^{49} + 7090402148994843433389 q^{50} - 4513112362705442454168 q^{51} - 22382594735756022154492 q^{52} + 3154362018989061130974 q^{53} - 14408091761318607149596 q^{54} + 11360707240851824399304 q^{55} + 14696779904127968977743 q^{56} + 24146248175223156466960 q^{57} - 40660216441227163832130 q^{58} - 81754126111915820731956 q^{59} + 122151699670622343074528 q^{60} - 36805153275262856581978 q^{61} + 142022375564892438347916 q^{62} + 17045317221103933287533 q^{63} + 172048781792046512913217 q^{64} - 163672145104218353792700 q^{65} - 347644219188679267923520 q^{66} + 202844281032408711974708 q^{67} + 26456739082621858621926 q^{68} - 230547072661305668895744 q^{69} + 85201832816584462566756 q^{70} + 426799501619955783974856 q^{71} + 212306425828334311742175 q^{72} - 330816419355757116007006 q^{73} - 426549788486578565156874 q^{74} - 45667218739968981225460 q^{75} - 473367544668166753122742 q^{76} - 85388845479088340288148 q^{77} - 1397985294248503611540232 q^{78} - 35566967774975220998800 q^{79} + 3842081036762216597201184 q^{80} - 124911371057262819572699 q^{81} + 457095253243023963414546 q^{82} - 455154069535425887019036 q^{83} - 2478641088545930906861690 q^{84} - 6046723725233892028937028 q^{85} + 7344585941643695489970048 q^{86} + 5634968273069989674763480 q^{87} - 5661815594567657354110080 q^{88} + 6442395074441133130075698 q^{89} - 9078749342974343005887868 q^{90} - 1123360480171883676016882 q^{91} - 11197484809271874469715232 q^{92} + 617486552550882891215808 q^{93} + 14977336705402578057903684 q^{94} - 2714436834332826037236648 q^{95} + 8002766421098256422847106 q^{96} + 1775035154391824538769178 q^{97} + 793721041609686654863343 q^{98} + 30176369524459678103752684 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(7))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7
7.26.a.a 7.a 1.a $6$ $27.720$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-4230\) \(-72104\) \(110161332\) \(-83047723206\) $+$ $\mathrm{SU}(2)$ \(q+(-705-\beta _{1})q^{2}+(-12017+2\beta _{1}+\cdots)q^{3}+\cdots\)
7.26.a.b 7.a 1.a $7$ $27.720$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(8373\) \(-599172\) \(485320794\) \(96889010407\) $-$ $\mathrm{SU}(2)$ \(q+(1196+\beta _{1})q^{2}+(-85596+3\beta _{1}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(7))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_0(7)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)