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Properties

Label 306.4.r
Level $306$
Weight $4$
Character orbit 306.r
Rep. character $\chi_{306}(25,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $432$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 306 = 2 \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 306.r (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 153 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(306, [\chi])\).

Total New Old
Modular forms 1328 432 896
Cusp forms 1264 432 832
Eisenstein series 64 0 64

Trace form

\( 432 q - 20 q^{9} + O(q^{10}) \) \( 432 q - 20 q^{9} - 100 q^{11} + 32 q^{12} + 496 q^{15} + 3456 q^{16} + 224 q^{18} + 336 q^{23} - 160 q^{24} - 552 q^{27} + 496 q^{33} + 2240 q^{35} - 80 q^{36} - 2528 q^{39} - 1920 q^{41} - 528 q^{42} + 684 q^{43} + 256 q^{44} + 2464 q^{45} + 2800 q^{50} + 3488 q^{51} + 2816 q^{53} + 584 q^{54} - 964 q^{57} - 764 q^{59} + 2048 q^{60} - 5184 q^{62} - 3640 q^{63} + 2560 q^{65} - 760 q^{66} - 2080 q^{69} - 1280 q^{71} - 492 q^{75} - 3552 q^{77} + 4736 q^{78} - 3312 q^{82} - 1928 q^{83} - 320 q^{84} - 3312 q^{85} - 6880 q^{86} - 1040 q^{87} + 288 q^{88} + 3984 q^{90} + 4032 q^{91} + 2496 q^{93} - 6520 q^{95} - 36 q^{97} + 26860 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(306, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(306, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(306, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 2}\)