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Properties

Label 325.6.n
Level $325$
Weight $6$
Character orbit 325.n
Rep. character $\chi_{325}(101,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $214$
Sturm bound $210$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(210\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(325, [\chi])\).

Total New Old
Modular forms 364 226 138
Cusp forms 340 214 126
Eisenstein series 24 12 12

Trace form

\( 214 q + 3 q^{2} - 8 q^{3} + 1633 q^{4} + 162 q^{6} - 270 q^{7} - 8047 q^{9} + O(q^{10}) \) \( 214 q + 3 q^{2} - 8 q^{3} + 1633 q^{4} + 162 q^{6} - 270 q^{7} - 8047 q^{9} - 306 q^{11} + 584 q^{12} + 215 q^{13} - 4052 q^{14} - 21931 q^{16} + 2267 q^{17} + 1722 q^{19} + 1670 q^{22} + 5744 q^{23} + 19494 q^{24} - 833 q^{26} + 18028 q^{27} - 28470 q^{28} + 5331 q^{29} + 12129 q^{32} + 27180 q^{33} + 109335 q^{36} - 10485 q^{37} + 6688 q^{38} - 22954 q^{39} - 38865 q^{41} + 15130 q^{42} + 27098 q^{43} - 88266 q^{46} - 90630 q^{48} + 220069 q^{49} + 57068 q^{51} - 63832 q^{52} - 53014 q^{53} - 139320 q^{54} - 106670 q^{56} - 133569 q^{58} + 71964 q^{59} + 4521 q^{61} - 8346 q^{62} + 372600 q^{63} - 515998 q^{64} + 366640 q^{66} + 130044 q^{67} - 139777 q^{68} + 25434 q^{69} + 185160 q^{71} - 341433 q^{72} - 44317 q^{74} - 267066 q^{76} - 279520 q^{77} + 147454 q^{78} - 555472 q^{79} - 360907 q^{81} + 107091 q^{82} - 432444 q^{84} - 8604 q^{87} - 202390 q^{88} + 365238 q^{89} - 230246 q^{91} + 1467728 q^{92} + 445272 q^{93} + 286020 q^{94} - 41112 q^{97} + 236829 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(325, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(325, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(325, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)