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Properties

Label 245.4.q
Level $245$
Weight $4$
Character orbit 245.q
Rep. character $\chi_{245}(11,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $672$
Newform subspaces $2$
Sturm bound $112$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.q (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 2 \)
Sturm bound: \(112\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(245, [\chi])\).

Total New Old
Modular forms 1032 672 360
Cusp forms 984 672 312
Eisenstein series 48 0 48

Trace form

\( 672 q - 12 q^{3} + 224 q^{4} - 10 q^{5} + 20 q^{6} + 68 q^{7} + 392 q^{9} + O(q^{10}) \) \( 672 q - 12 q^{3} + 224 q^{4} - 10 q^{5} + 20 q^{6} + 68 q^{7} + 392 q^{9} - 20 q^{10} + 14 q^{11} + 736 q^{12} - 48 q^{13} + 280 q^{14} + 924 q^{16} - 132 q^{17} + 42 q^{18} + 18 q^{19} + 280 q^{20} - 242 q^{21} - 392 q^{22} + 672 q^{23} + 1988 q^{24} + 1400 q^{25} - 254 q^{26} + 924 q^{27} - 518 q^{28} - 42 q^{29} - 140 q^{30} + 168 q^{31} - 420 q^{32} - 320 q^{33} - 2140 q^{34} - 800 q^{35} - 6272 q^{36} + 560 q^{37} + 3568 q^{38} - 756 q^{39} - 240 q^{40} + 608 q^{41} + 4482 q^{42} + 952 q^{43} - 3878 q^{44} - 600 q^{45} - 3822 q^{46} - 2276 q^{47} - 18980 q^{48} - 3554 q^{49} - 1904 q^{51} - 14332 q^{52} - 1596 q^{53} - 1584 q^{54} + 640 q^{55} - 1364 q^{56} - 1960 q^{57} + 5054 q^{58} + 1006 q^{59} + 3920 q^{60} + 782 q^{61} + 7144 q^{62} + 616 q^{63} - 5040 q^{64} - 210 q^{65} - 4046 q^{66} + 308 q^{67} + 6728 q^{68} + 7596 q^{69} - 1600 q^{70} - 1288 q^{71} - 294 q^{72} + 1532 q^{73} - 3290 q^{74} - 300 q^{75} - 852 q^{76} + 3696 q^{77} - 6020 q^{78} + 700 q^{79} + 6560 q^{80} + 30982 q^{81} + 22070 q^{82} + 7716 q^{83} + 27056 q^{84} + 560 q^{85} + 5838 q^{86} + 4596 q^{87} - 2954 q^{88} + 658 q^{89} - 540 q^{90} + 14654 q^{91} - 17388 q^{92} - 924 q^{93} - 10610 q^{94} + 280 q^{95} - 22814 q^{96} - 12608 q^{97} - 20310 q^{98} + 7868 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(245, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
245.4.q.a 245.q 49.g $324$ $14.455$ None \(-2\) \(-6\) \(135\) \(6\) $\mathrm{SU}(2)[C_{21}]$
245.4.q.b 245.q 49.g $348$ $14.455$ None \(2\) \(-6\) \(-145\) \(62\) $\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{4}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(245, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)