Properties

Label 6.25.b
Level $6$
Weight $25$
Character orbit 6.b
Rep. character $\chi_{6}(5,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $25$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 25 \)
Character orbit: \([\chi]\) \(=\) 6.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(25\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{25}(6, [\chi])\).

Total New Old
Modular forms 26 8 18
Cusp forms 22 8 14
Eisenstein series 4 0 4

Trace form

\( 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9} + O(q^{10}) \) \( 8 q - 131880 q^{3} - 67108864 q^{4} + 33718272 q^{6} - 10160794640 q^{7} + 295169053896 q^{9} - 1863369424896 q^{10} + 1106289623040 q^{12} + 50568363679120 q^{13} - 348034956760512 q^{15} + 562949953421312 q^{16} - 514738292981760 q^{18} - 978083631341264 q^{19} + 3640012304241936 q^{21} - 336450979430400 q^{22} - 282849366245376 q^{24} + 7630618767014024 q^{25} - 86594528606057640 q^{27} + 85234923203461120 q^{28} - 725410188900237312 q^{30} + 3092119786822709104 q^{31} - 8158685952668529600 q^{33} + 3821138032531341312 q^{34} - 2476057486864416768 q^{36} + 22590293223992782480 q^{37} - 40190176581881465040 q^{39} + 15631075664637984768 q^{40} - 79119883835565342720 q^{42} + 226487466371803896880 q^{43} - 347709996757177504128 q^{45} + 139842130561120468992 q^{46} - 9280229982150328320 q^{48} + 104686700473616731800 q^{49} + 558091874936566543104 q^{51} - 424198180105575464960 q^{52} + 334066775626796728320 q^{54} - 2212687664250467338368 q^{55} + 3588879995640760725840 q^{57} - 1867706355469718323200 q^{58} + 2919528822560885047296 q^{60} - 6507010783838092385648 q^{61} + 10112982777612899380080 q^{63} - 4722366482869645213696 q^{64} - 1924112442339530440704 q^{66} - 7042120118150060144720 q^{67} - 4323335967368731345536 q^{69} + 16481910236435553583104 q^{70} + 4317937762413135790080 q^{72} + 36259820324758576687120 q^{73} - 108081978448612908655272 q^{75} + 8204760174538377920512 q^{76} - 74188898027329578270720 q^{78} + 316807052777330015315824 q^{79} - 268518660504396776813304 q^{81} + 83114941529654645882880 q^{82} - 30534636335462338265088 q^{84} - 222512862545524200678912 q^{85} + 449461577201807342128320 q^{87} + 2822355377657688883200 q^{88} + 612683975543382025371648 q^{90} - 1196839602335690774367520 q^{91} + 873237537450828783745680 q^{93} - 1298887117621773403422720 q^{94} + 2372712456480891076608 q^{96} + 816517576248201265716880 q^{97} + 695858883367208922313344 q^{99} + O(q^{100}) \)

Decomposition of \(S_{25}^{\mathrm{new}}(6, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
6.25.b.a \(8\) \(21.898\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-131880\) \(0\) \(-10160794640\) \(q+\beta _{1}q^{2}+(-16485-\beta _{1}-\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{25}^{\mathrm{old}}(6, [\chi])\) into lower level spaces

\( S_{25}^{\mathrm{old}}(6, [\chi]) \cong \) \(S_{25}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)