Properties

Label 7.22.a
Level $7$
Weight $22$
Character orbit 7.a
Rep. character $\chi_{7}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $2$
Sturm bound $14$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 7.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(14\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(7))\).

Total New Old
Modular forms 15 11 4
Cusp forms 13 11 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
\(+\)\(5\)
\(-\)\(6\)

Trace form

\( 11 q + 287 q^{2} + 257686 q^{3} + 15809161 q^{4} - 63281864 q^{5} + 20290814 q^{6} + 282475249 q^{7} + 4103699055 q^{8} + 50006802667 q^{9} + O(q^{10}) \) \( 11 q + 287 q^{2} + 257686 q^{3} + 15809161 q^{4} - 63281864 q^{5} + 20290814 q^{6} + 282475249 q^{7} + 4103699055 q^{8} + 50006802667 q^{9} + 44269189204 q^{10} + 53191743976 q^{11} + 206480040662 q^{12} - 173662063204 q^{13} + 1368027630907 q^{14} + 4381319269888 q^{15} + 8438757071329 q^{16} - 5535353986398 q^{17} - 34196618583049 q^{18} - 5494935211558 q^{19} - 181898676998248 q^{20} + 76072279407194 q^{21} + 311547897098824 q^{22} + 347358696320496 q^{23} + 319153590439602 q^{24} + 1535576027170153 q^{25} - 720307893638368 q^{26} + 2662576846532020 q^{27} - 1110800867088367 q^{28} + 4849545159076318 q^{29} - 14927779067899888 q^{30} - 10691109957426708 q^{31} + 11868609655602127 q^{32} - 26781225254493488 q^{33} + 2246800485951138 q^{34} + 16143903401540432 q^{35} + 172457990753826761 q^{36} - 74778332232037098 q^{37} - 205268007642555310 q^{38} + 100019441561005288 q^{39} - 169465653843227184 q^{40} + 29586335072215250 q^{41} + 203283409549385158 q^{42} + 533480505501994576 q^{43} - 652483865050083520 q^{44} - 1563040398841319240 q^{45} + 901386648804565008 q^{46} - 1059213113920171548 q^{47} + 3197480240340600926 q^{48} + 877714929273732011 q^{49} + 969710831904750349 q^{50} - 1618025303650537692 q^{51} + 31897784716424452 q^{52} - 3354384351079501614 q^{53} + 2786636031139308644 q^{54} + 1481132629859277824 q^{55} + 1794848943117392463 q^{56} - 1128176350909108220 q^{57} + 7101472695097825870 q^{58} + 7183978615610091234 q^{59} - 28877066152405052512 q^{60} - 5629674914955952912 q^{61} - 21498886426604098836 q^{62} - 5866451136856878463 q^{63} - 28059757735216506847 q^{64} + 9485762772220105840 q^{65} + 118085268087815526752 q^{66} - 6035357847576403948 q^{67} - 16372673728283654586 q^{68} + 40746026409083183424 q^{69} - 37181714941933516444 q^{70} + 28065118041679869312 q^{71} + 13153529348221037055 q^{72} + 25365012842597517126 q^{73} - 103059192765738253722 q^{74} - 493284906537314350 q^{75} - 184251057634957793942 q^{76} + 48827180725908055688 q^{77} + 1026861031589297912 q^{78} + 33657865163468253400 q^{79} - 359791216574016831616 q^{80} + 504760583855001142519 q^{81} + 197652174229769129234 q^{82} + 179411145690403571826 q^{83} + 187180021529307607654 q^{84} + 313537119570937305072 q^{85} - 57189673024170868496 q^{86} - 1671832042458458239460 q^{87} + 990289623305993605680 q^{88} - 434115879238077635762 q^{89} + 330651619946256160772 q^{90} + 152227986404659350220 q^{91} - 890380388725635019008 q^{92} - 984408211886598553608 q^{93} - 125830565410079247324 q^{94} + 1253026376960724092992 q^{95} - 1896623874184902767198 q^{96} - 477518868817518026478 q^{97} + 22900380427414644287 q^{98} - 484685185597480418648 q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(7))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7
7.22.a.a 7.a 1.a $5$ $19.563$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 7.22.a.a \(-2278\) \(-5810\) \(-60216716\) \(-1412376245\) $+$ $\mathrm{SU}(2)$ \(q+(-456+\beta _{1})q^{2}+(-1155-18\beta _{1}+\cdots)q^{3}+\cdots\)
7.22.a.b 7.a 1.a $6$ $19.563$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 7.22.a.b \(2565\) \(263496\) \(-3065148\) \(1694851494\) $-$ $\mathrm{SU}(2)$ \(q+(428-\beta _{1})q^{2}+(43924-15\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(7))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(7)) \simeq \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)